International Journal of Mathematics and Soft Computing

1-11

Authors: Lekha Bijukumar, Avani Matad

A graph $G=(V(G),E(G))$ with $p$ vertices and $q$ edges is said to be an \textit{odd mean graph} if there is an injection $\textit{f}:V(G)\rightarrow\{0,1,2,\ldots,2q-1\}$ and the induced function $\textit{f*}:E(G)\rightarrow\{1,3,5,\ldots,2q-1\}$ defined as $f*(uv)=\begin{cases} \frac{f(u)+f(v)}{2}; \, \text{ if } f(u)+f(v) \text{ is even}\\ \frac{f(u)+f(v)+1}{2}; \, \text{ if } f(u)+f(v) \text{ is odd} \end{cases}$ is a bijection. In this paper we investigate some new families of odd mean graphs.

23-31

Authors: Gaurang V Ghodasara, Divya G Adalja

A graph $G=(V,E)$ is said to have a divisor cordial labeling if there is a bijection $f :V(G)\rightarrow\{1,2,\ldots|V(G)|\}$ such that if each edge $e=uv$ is assigned the label 1 if $f(u) | f(v) $ or $ f(v)| f(u)$ and 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. If a graph has a divisor cordial labeling, then it is called divisor cordial graph. In this paper we derive divisor cordial labeling of ring sum of different graphs.

43-50

Authors: S K Vaidya, R M Pandit

A set $F \subseteq E(G) $ is an edge dominating set if each edge in $E(G)$ is either in $F$ or is adjacent to an edge in $F$. An edge dominating set $F$ is called a minimal edge dominating set if no proper subset $F ^ \prime$ of $F$ is an edge dominating set. The edge domination number $\gamma ^\prime(G)$ is the minimum cardinality among all minimal edge dominating sets. We investigate the edge domination number of some graphs called snakes which are obtained from path $P_n$ by replacing its edges by cycles $C_3$ and $C_4$.

57-63

Authors: K Monika, K Murugan

A $(p,q)$ graph $G=(V,E)$ is said to be an odd-even sum graph if there exists an injective function $f:V(G)\rightarrow\lbrace\pm 1,\pm 3 \pm 5, ...,\pm (2p-1)\rbrace$ such that the induced mapping $f^{*}:E(G)\rightarrow\lbrace 2,4,6, ...,2q\rbrace$ defined by $f^{*}(uv)=f(u)+f(v)~\forall~uv\in E(G)$ is bijective. The function $f$ is called an odd-even sum labeling of $G$. In this paper we study odd-even sum labeling of path $P_{n}(n\geq2)$, star $K_{1,n}(n\geq 1)$, bistar $B_{m,n}$,$S(K_{1,n})$, $B(m,n,k)$ and some standard graphs.

75-87

Authors: K Chitra Lakshmi, K Nagarajan

Let $G =(V,E)$ be a graph and $f$ be a mapping from $V(G) \rightarrow \left\{0,1,2 \right\}$. For each edge $uv$ assign the label \(\left\lceil\sqrt{f(u)f(v)}\right\rceil\), $f$ is called a geometric mean cordial labeling if $\mid v_f (i)- v_f (j)\mid \leq 1 $ and $\mid e_f (i)- e_f (j) \mid \leq1 $, where $v_f(x)$ and $e_f(x)$ denote the number of vertices and edges labeled with $x$, $x \in\left\{ 0,1,2 \right\}$ respectively. A graph with a geometric mean cordial labeling is called geometric mean cordial graph. In this paper geometric mean cordiality of some standard graphs such as path, star, cycle, complete graph, complete bipartite graph, wheel are discussed.

95-108

Authors: Ch Santhi Sundar Raj, S Nageswara Rao, M Santhi, K Ramanuja Rao

The notion of an Almost Distributive Lattice (abbreviated as ADL) is a common abstraction of several lattice theoretic generalization of Boolean algebras and Boolean rings. In this paper we introduce the notion of Relative pseudo-complementation on ADL's and discuss several properties of this.

117-125

Authors: U M Prajapati, B N Suthar

In this paper, we investigate prime labeling for some graphs obtained by duplication of graph elements and also we derive some result for $K_{2,n}$.Graph labeling, prime labeling, prime graph.

1-11

Authors: R Murali, A Antony Raj, S Sudha

In this paper, we prove the Hyers-Ulam stability of the cubic and quartic functional equations in matrix paranormed spaces.

21-32

Authors: K Radha, Natesan Kumaravel

In this paper, a necessary and sufficient condition for the cartesian product and composition of two edge regular fuzzy graphs to be an edge regular fuzzy graph is determined.

43-56

Authors: Ujwala Deshmukh, Smita Amogh Bhatavadekar

In this paper we prove that arbitrary supersubdivision of ladder, cyclic ladder, triangular snake and certain double triangular snake are cordial.

65-73

Authors: U M Prajapati, R M Gajjar

Let $G = (V(G) , E(G))$ be a graph and let $\displaystyle f:V(G)\rightarrow \{0,1\}$ be a mapping from the set of vertices to \{0,1\} and for each edge $uv \in E$ assign the label $|f(u)-f(v)|$. If the number of vertices labeled with 0 and the number of vertices labeled with 1 differ by at most 1 and the number of edges labled with 0 and the number of edges labeled with 1 differ by at most 1, then $f$ is called a cordial labeling. In this paper we discuss cordial labeling for duplication of certain graph element of cycle graph and path graph.

87-95

Authors: G Britto Antony Xavier, T. G Gerly

In this paper, we extend certain results of finite $q$-alpha multi-series to infinite $q$-alpha multi-series and obtain the sum of infinite $q$-alpha multi-series of polynomials, polynomial factorials and logarithmic functions.

105-110

Authors: N Murugesan, R Anitha

By (d, d+1) - regular graph, we mean a graph whose vertices are all having degree either d or d+1. Two graphs are said to be sequentially equivalent (SE) if they have the same degree sequence. In this paper, we discuss some extremal problems of general (d, d+1) -regular graphs, and SE (d, d+1) - regular graphs.

121-130

Authors: S Abirami, S Murugesan

In this paper, the concepts of an intuitionistic fuzzy semihyperrings and an intuitionistic fuzzy subsemihypermodule of R, where R is a semihyperring, are introduced and some of their characteristics are proved. In particular, fully idempotent semihyperrings are investigated in the context of intuitionistic fuzzy concept.

1-9

Authors: Hariwan Zikri Ibrahim, A Mizyed

In this paper, we introduce and study the notion of semi-$\gamma$-$I$-open sets in ideal topological spaces and investigate some of their properties. Further, we study continuous functions on the above set and derive some of their properties.

29-38

Authors: Venkiteshwaran Sujitha

For a connected graph $G=(V,E)$, a set $S \subseteq E$ is called an \textit{edge-to-vertex geodetic set} of $G$ if every vertex of $G$ is either incident with an edge of $S$ or lies on a geodesic joining some pair of edges of $S$. The minimum cardinality of an edge-to-vertex geodetic set of $G$ is $g_{ev}(G)$. Any edge-to-vertex geodetic set of cardinality $g_{ev}(G)$ is called an \emph{edge-to-vertex geodetic basis} of $G$. A subset $T \subseteq S$ is called a \emph{forcing} subset for $S$ if $S$ is the unique minimum edge-to-vertex geodetic set containing $T$. A forcing subset for $S$ of minimum cardinality is a minimum forcing subset of $S$. The \emph{forcing edge-to-vertex geodetic number} of $S$, denoted by $f_{ev}(S)$, is the cardinality of a minimum forcing subset of $S$. The \emph{upper forcing edge-to-vertex geodetic number} of $G$, denoted by $f^{+}_{ev}(G)$, is $f^{+}_{ev}(G) = max \left\{f_{ev}(S)\right\}$, where the maximum is taken over all minimum edge-to-vertex geodetic sets $S$ in $G$. It is shown that the upper forcing edge-to-vertex geodetic number lies between 0 and $g_{ev}(G)$. Also, the upper forcing edge-to-vertex geodetic number of certain classes of graphs such as cycle, tree, complete graph and complete bipartite graph are determined.

49-56

Authors: V Kokilavani, M Vivek Prabu

In this paper, we define some new sets namely soft semi $^\#g\alpha$-border, soft semi $^\#g\alpha$-frontier and soft semi $^\#g\alpha$-exterior which are denoted by $\widetilde{s}$semi $^\#g\alpha$-bd(F,A), $\widetilde{s}$semi $^\#g\alpha$-fr(F,A) and $\widetilde{s}$semi $^\#g\alpha$-ext(F,A), where (F,A) is any soft set of (X,E) and also investigate their basic properties.

81-91

Authors: Medha Itagi Huilgol, Chitra Ramprakash

The concept of edge rotations and distance between graphs was introduced by Gary Chartrand et al. A graph $G$ can be transformed into a graph $H$ by an edge rotation if $G$ contains distinct vertices $u$,$v$ and $w$ such that $uv$ $\in $ $E(G)$, $uw$ $\notin$ $E(G)$ and $H$ $\cong$ $G - uv + uw$. In this paper we consider rotations on some snake related graphs followed by some general results.

107-120

Authors: Alias B Khalaf, Hariwan Zikri Ibrahim

In this paper, we introduce the notions of $\alpha_{\gamma}$-interior, $\alpha_{\gamma}$-neighbourhood, $\alpha_{\gamma}$-derived, $\alpha_{\gamma}$-boundary, $\alpha_{\gamma}$-kernel and $\alpha$-$\gamma$-g.closed set defined by $\gamma$-operation on $\alpha O(X)$ and investigate some of their properties.

133-142

Authors: S K Vaidya, N J Kothari

The concept of equi independent equitable domination is the combination of two important concepts, namely independent domination and equitable domination. A subset $D$ of $V(G)$ is called an equitable dominating set if for every $v \in V(G)-D$, there exists a vertex $u \in D$ such that $uv \in E(G)$ and $|deg(u)-deg(v)|\leq 1$. A vertex subset $D$ is said to be equitable independent set if any two vertices of $D$ are either non adjacent or if adjacent then their degrees differ by atleast 2. An equitable dominating set $D$ is said to be an equi independent equitable dominating set if it is also equitable independent set. The equi independent equitable domination number $i^e$ is the minimum cardinality of an equi independent equitable dominating set.

153-162

Authors: Haresh V Dedania, Milan Kantilal Kansagara

Let $G$ be an LCA group, $\om$ be a weight function on $G$, and $\A$ be a semisimple, commutative Banach algebra. We characterize some Banach algebra properties of vector-valued Beurling algebra $\Lgwa$ in terms of $\Lgw$ and $\A$ using the Bochner integration theory. These properties are unique uniform norm property (UUNP), unique $C^{\ast}$-norm property (UC$^{\ast}$NP), quasi divisor of zero property (QDZP), weak regularity (WR), regularity, and complete regularity (CR).

173-182

Authors: S S Sandhya, S Somasundaram, S Anusa

Let $G$ be a $(p,q)$ graph and $f:V(G)\leftarrow \{1,2,3,…,p+q \}$ be an injective function. For each edge $e=uv$ , let $f^*(e=uv)=\lceil \sqrt{\frac{f(u)^2+f(v)^2}{2}} \rceil$ or =\lfloor\sqrt{\frac{f(u)^2+f(v)^2}{2}} \rfloor$, then $f$ is called a super root square mean labeling if $f(V) \cup \{f^*(e):e \in E(G) \}=\{1,2,…,p+q \}. A graph that admits a super root square mean labeling is called as super root square mean graph. In this paper we prove that Double triangular snake, Alternate double triangular snake, Double quadrilateral snake and Alternate Double uadrilateral snake graphs are super root square mean graphs. Keywords: Root Square mean graph, Super Root Square mean graph, Triangular snake, Double triangular snake, Quadrilateral snake, Double quadrilateral snake.

1-7

Authors: R Vasanthi, K Subramanian

A set $D \subseteq V$ of vertices in a graph $G=(V, E)$ is called a dominating set if every vertex in $V-D$ is adjacent to a vertex in $D$. A set $C \subseteq V$ of vertices in $G$ is called a vertex covering set if every edge of $G$ is incident to at least one vertex in $C$. Also $C$ is said to be a minimum vertex covering set if there is no other vertex covering set $C^\prime$ such that $\left|C'\right| \textless \left|C\right|$. A dominating set which intersects every minimum vertex covering set in $G$ is called a vertex covering transversal dominating set. The minimum cardinality of a vertex covering transversal dominating set is called vertex covering transversal domination number of $G$ and is denoted by $\gamma_{vct}(G)$. In this paper, we begin with an investigation of this parameter.

15-19

Authors: S K Vaidya, R N Mehta

For a non - empty set W of vertices in a connected graph G, the steiner distance d(W) of W is the minimum size of a connected subgraph G containing W. Necessarily, each such subgraph is a tree and is called a steiner tree or a steiner W - tree. The set of all vertices of G that lie on some steiner W - tree is denoted by S(W). If S(W) = V (G) then W is called a steiner set for G. The steiner number s(G) is the minimum cardinality of a steiner set. The minimum cardinality of a steiner dominating set is called the steiner domination number of graph.

29-37

Authors: S Sudha, Varatharajan Kanniga

In this paper we have shown that the the splitting graph of the complete bi-partite graph $K_{m,\;n}$ is graceful and the tensor product of the complete bi-partite graph $K_{m,\;n}$ and a path graph $P_k (k>1)$ is also graceful.

51-57

Authors: A Ponmoni, S Navaneetha Krishnan, A Nagarajan

For a graph total edge Lucas irregular labeling f :V(G) E (G)  {1,2,…,K} is defined as a labeling on V(G) and E (G) in such a way that for any two different edges and , their weights and are distinct Lucas numbers.The total edge Lucas irregularity strength, tels(G), is defined as the minimum K for which G has total edge Lucas irregular labeling. In this paper we prove the graphs , Cn ,K1,n and Book (with 3 sides and 4 sides) admits total edge Lucas irregular labeling and we determine the total edge Lucas irregularity strength for those graphs.

69-74

Authors: Purity Jebotibin Kiptum, Joseph E Esekon, Owino Maurice Oduor

Derivatives are used in hedging European options against risks. The partial derivatives of the solution to either a variable or a parameter in the Black-Scholes model are called risk (Greek) parameters or simply the Greeks. Nonlinear versions of the standard Black-Scholes Partial Differential Equations have been introduced in financial mathematics in order to deal with illiquid markets. In this paper we derive the Greek parameters of a nonlinearBlack-Scholes Partial Differential Equation whose nonlinearity is as a result of transaction costs for modeling illiquid markets. We compute the Greek parameters of a European call option price from the nonlinear equation $u_t + \frac{1}{2}\sigma^2S^2u_{SS}(1+2\rho Su_{SS})= 0$. All these Greeks were of the form $a+\dfrac{1}{\rho} f(S,t)$. The methodology involved deriving the Greek parameters from the formula of the equation by differentiating the formula with respect to either a variable or a parameter. These Greeks may help a trader to hedge risks in a non-ideal market situation.

83-90

Authors: U D Tapi, A. Deole Bhagyashri

In this paper we introduce the concepts of fuzzy semi-connectedness and fuzzy pre- connectedness in fuzzy Čech closure space and study some of their fundamental properties.

105-114

Authors: K Lakshmiprabha, K Nagarajan

In this paper, the two major fields of graph theory namely decomposition and domination are connected and new concept called Ascending Domination Decomposition ($ADD$) of a graph $G$ is introduced. An $ADD$ of a graph $G$ is a collection $\psi=\{G_{1},G_{2},\ldots,G_{n}\}$ of subgraphs of $G$ such that, each $G_{i}$ is connected, every edge of $G$ is in exactly one $G_{i}$ and $\gamma(G_{i})=i$, $1\leq i\leq n$. In this paper, we prove the subdivision of some standard graphs admit $ADD$.

127-134

Authors: Md Rokonuzzaman, Md Shakhawat Hossain

In this study, chi-square mixture of t-moment distribution has been defined and also determined its different moments and shape characteristics. Mean of this mixture distribution is zero. This distribution is found to be symmetrical about mean and bimodal.

145-153

Authors: N R Santhi Maheswari, C Sekar

In this paper, dm-degree and total dm-degree of a vertex in fuzzy graphs, m- neighbourly irregular fuzzy graphs and m- neighbourly totally irregular fuzzy graphs are introduced. Some properties on m-neighbourly irregular fuzzy graphs are also discussed in this paper. Comparative study between m- neighbourly irregular fuzzy graphs and m- neighbourly totally irregular fuzzy graphs is done and m- neighbourly irregularity on some fuzzy graphs whose underlying crisp graphs are a cycle and a path is also studied.

165-172

Authors: Samuel Mary Jemima, Rajkumar Dare

Watson-Crick finite automata are language recognizing devices similar to finite automata introduced in DNA computing area. Local languages are of great interest in the study of formal languages using factors of length two or more. We define Watson-Crick local languages using double stranded sequences where the two strands relate to each other through a complementary relation inspired by the DNA complementarity. We also define tiling recognizable Watson-Crick local languages and prove some closure properties. We also extend Watson-Crick local languages to finite arrays and prove some closure properties.

183-187

Authors: C Sivagnanam, M P Kulandaivel

A subset $S$ of $V$ is called a dominating set in $G$ if every vertex in $V-S$ is adjacent to at least one vertex in $S$. A dominating set $S$ is said to be a restrained dominating set if $\langle V-S \rangle$ contains no isolated vertices. The minimum cardinality of a restrained dominating set of $G$ is called the restrained domination number of $G$ and is denoted by $\gamma_{r}(G)$. The connectivity $\kappa(G)$ of a graph $G$ is the minimum number of vertices whose removal results in a disconnected or trivial graph. In this paper we characterized the graphs with sum of restrained domination number and connectivity is equal to $2n-6$.

197-212

Authors: Rhoda Ong'awa Esilaba, Edgar O Otumba, Alfred W Manyonge

Nash equilibrium is the central solution concept with diverse applications for most gamesin game theory. For games with multiple equilibria, different equilibria can have different rewards for the players thus causing a challenge on their choice of strategies. The computation of most efficient Nash Equilibrium in games can be applied to most situations in competitive Economic environment that are faced with multiple choices on which strategy is optimal.

1-10

Authors: C Janaki, D Sreeja

This paper focuses on soft πgb-closed sets and soft πgb-open sets in soft topological spaces and to investigate its properties. Further soft πgb-T1/2 space is introduced and its basic properties are discussed.

17-21

Authors: P Nageswari, P.B Sarasija

The energy of the graph G is defined as the sum of the absolute values of its eigenvalues. In this paper, we study the energy of the generalised star graphs. The purpose of the paper is to study the bounds of the eigenvalues and energy of the generalised star graphs.

31-44

Authors: Gunjan Tripathi, K. C Tripathi, A. P Dwivedi

In this paper, we have considered the two sets of triple series equations of the first kind and second kind, which are the generalization of dual series equations involving Associated Legendre functions and solved the two sets of series equations involving a spherical or spheroidal boundary when different conditions are prescribed on different parts of the boundary.

57-64

Authors: Selvam Avadayappan, M Bhuvaneshwari

The graph S(G) obtained from a graph G(V,E), by adding a new vertex w for every vertex v  V and joining w to all neighbours of v in G, is called the splitting graph of G. The cosplitting graph CS(G) is obtained from G, by adding a new vertex w for each vertex v  V and joining w to those vertices of G which are not adjacent to v in G. In this paper, we introduce the concept of cosplitting graph and characterise the graphs for which splitting and cosplitting graphs are isomorphic.

79-92

Authors: Mijanur Rahaman Seikh, Prasun Kumar Nayak, Madhumangal Pal

In this paper, two-person matrix games is considered whose elements of pay-off matrix are triangular fuzzy numbers (TFNs). To solve such game a new method based on _-cut of TFN is developed for each of the players. In this method, two auxiliary bi-objective linear programming (BOLP) models are derived. Then using average weighted approach these two BOLP models are decomposed into two auxiliary crisp linear programming (LP) problems. Finally, the value of the matrix game for each player is obtained by solving two corresponding auxiliary LP problems using the existing simplex method. Validity and applicability of this method are illustrated with practical example compared to existing methods.

105-109

Authors: Rao Li

In this paper, using the upper bound for the spectral radius for a graph obtained by Cao, we present sufficient conditions based on the spectral radius for a graph to contain some subgraphs.

119-127

Authors: T Tharmaraj, P.B Sarasija

A graph is said to be a square graceful graph if there exists an injection such that the induced mapping by is a bijection. The function f is called a square graceful labeling of G. In this paper, we prove the graph obtained by the subdivision of the edges of stars of bistar , the graph obtained by the subdivision of the edges of bistar , the graph obtained by the subdivision of the edges of the path in a comb , , and are square graceful graph. ) , ( qp) , (EVG} ,..., 3,2,1,0{) ( : 2 q G V f  } ,..., 9,4,1{) ( : 2 q G E f p  | ) () (| ) (vf uf uvf p   n m B , n m B , n P 1 K P n   n K C , 13 *   m S n :   n K C , 13 ,

143-153

Authors: C Sivagnanam

Let $G=(V,E)$ be a graph without isolated vertices. A dominating set $S$ of $G$ is a neighborhood total dominating set (ntd-set) if the induced subgraph $\left\langle N(S)\right\rangle$ of $G$ has no isolated vertices. The neighborhood total domination number $\gamma_{nt}(G)$ is the minimum cardinality of a ntd-set. The minimum number of colours required to colour all the vertices such that no two adjacent vertices have same colour is the chromatic number $\chi(G)$ of $G$. In this paper we find an upper bound for sum of the ntd-number and chromatic number and characterize the corresponding extremal graphs.

165-169

Authors: S K Vaidya, Rakhimol V. Isaac

A proper coloring of a graph G is called b-coloring if each color class contains a vertex which is adjacent to at least one vertex of every other color classes. We investigate b-chromatic number of some cycle and path related graphs.