International Journal of Mathematics and Soft Computing

11-18

Authors: M Selvi, D Ramya

A graph with vertices and edges is said to have skolem difference mean labeling if it is possible to label the vertices with distinct elements from in such a way that for each edge e = uv, let f*(e) = and the resulting labels of the edges are distinct and are from 1, 2, 3,…, q. A graph that admits a skolem difference mean labeling is called a skolem difference mean graph. In this paper, we prove that Tp-tree T, T  , T @ and T @ 2 where T is a Tp-tree are extra skolem difference mean graphs.

33-39

Authors: S K Vaidya, N H Shah

In this paper we prove that square graph and shadow graph of bistar admit cordial labeling. Moreover we prove that splitting graph of bistar as well as degree splitting graph of bistar are cordial graphs.

49-57

Authors: Muhammad Imran, Mehar Ali Malik, Muhmmad Yasir Hayat Malik

A $(p, q)$- simple graph is edge-magic if there exists a bijective function $\lambda:V(G)\cup E(G)\rightarrow \{1, 2, \dots, p+q\}$ such that $\lambda(u)+\lambda(uv)+\lambda(v)=k$, for all edge $uv\in E(G),$ where $k$ is called the magic constant or sometimes the valence of $\lambda$. An edge-magic total labeling $\lambda$ is called super edge-magic total if $\lambda(V(G))=\{1, 2, \dots, p\}$. In this paper, we construct new classes of trees using w-trees and generalized combs and prove that they admit super edge magic total labeling. We also prove that the extended umbrella graphs admit super edge-magic total labeling.

71-80

Authors: N. K Sudev, K. A Germina

Let $\mathbb{N}_0$ be the set of all non-negative integers and $\mathcal{P}(\mathbb{N}_0)$ be its power set. An integer additive set-indexer (IASI) is defined as an injective function $f:V(G)\to \mathcal{P}(\mathbb{N}_0)$ such that the induced function $f^+:E(G) \to \mathcal{P}(\mathbb{N}_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective, where $f(u)+ f(v)$ is the sum set of the sets $f(u)$ and $f(v)$. A graph $G$ which admits an IASI is called an IASI graph. An arithmetic integer additive set-indexer is an integer additive set-indexer $f$, under which the set-labels of all elements of a given graph $G$ are the sets whose elements are in arithmetic progressions. In this paper, we discuss the admissibility of arithmetic integer additive set-indexers by certain associated graphs of the given graph $G$, like line graph, total graph and the like.

95-104

Authors: D Antony Xavier, M Rosary, Andrew Arokiaraj

In this paper, we propose a new graph namely Sierpi_nski Gasket Rhombus SRn based on triangular graph like Sierpi_nski Gasket graph. Sierpi_nski Gasket Rhombus SRn is obtained by identifying two copies of Sierpi_nski Gasket graph along their side edges. Further we study some basic properties of Sierpi_nski Gasket Rhombus SRn and find hamiltonicity, pancyclicity and chromatic number of SRn.

113-127

Authors: S K Vaidya, M S Shukla

A \textit{b}-coloring by \textit{k}-colors is a proper coloring of the vertices of graph $\textit{G}$ such that in each color classes there exists a vertex that has neighbours in all the other $k-1$ color classes. The \textit{b}-chromatic number $\varphi (G)$ is the largest integer $\textit{k}$ for which $\textit{G}$ admits a \textit{b}-coloring with \textit{k}-colors. If $\chi (G)$ is the chromatic number of $\textit{G}$ then $\textit{G}$ is said to be \textit{b}-continuous if $b$-coloring exists for every integer $k$ satisfying $\chi \left( G \right) \le k \le \varphi \left( G \right)$. We investigate the \textit{b}-chromatic number of some cycle related graphs and also study their \textit{b}-continuity.

137-144

Authors: N.T Muthuraja, P Jeyanthi

A simple graph G = (V;E) admits an H-covering if every edge in E belongs to a subgraph of G isomorphic to H. G is H-magic if there is a total labeling f : V [ E ! f1; 2; 3; _ _ _ ; jV j + jEjg such that for each subgraph H0 = (V 0;E0) of G isomorphic to H,P v2V1 f(v) + P e2E1 f(e) = s is constant. When f(V ) = f1; 2; _ _ _ ; jV jg, then G is said to be H-supermagic. In this paper, we show that Pm;n and the splitting graph of a cycle Cn are cycle-supermagic.

153-164

Authors: Pradeep G Bhat, Sabitha D'Souza

Let $G$ be a graph with vertex set $V(G)$ and edge set $X(G)$ and consider the set $A=\{0,1\}$. A mapping $l:V(G)\longrightarrow A$ is called a binary vertex labeling of $G$ and $l(v)$ is called the label of the vertex $v$ under $l$. In this paper we introduce a new kind of graph energy for the binary labeled graph, the minimum covering label energy $E_{cl}(G)$. Depending on the underlying graph $G$ and its binary labeling, the upper and lower bounds for $E_{cl}(G)$ are established. The minimum covering label energies of complete and star graphs are computed. The characteristic polynomial of complete bipartite graph is also obtained.

173-181

Authors: Santhi Maheswari, C Sekar

A graph $G$ is said to be $(2, k)$-regular if $d_2(v) = k,$ for all $v$ in $G.$ A graph $G$ is said to be $(r, 2, k)$-regular if $d(v) = r$ and $d_2(v) = k,$ for all $v$ in $G.$ In this paper, we study some graph products in $(2,k)$-regular graph and ($r, 2, k)$- regular graph.

197-206

Authors: A Robert, S Pious Missier

In this paper, we introduce a new class of sets, namely semi*α-open sets, using α-open sets and the generalized closure operator. We find characterizations of semi*α-open sets. We also define the semi*α-interior of a subset. Further, we study some fundamental properties of semi*α-open sets and semi*α-interior.

213-224

Authors: S Kumaresan, R Bakthavachalam, K Krishnan, C Elango

In this paper we consider a continuous review perishable inventory system in Multi-echelon system, which is a building block for supply chain. A (s, Q) type perishable inventory system with Poisson demand and exponential distributed lead times for items are assumed at DC (middle echelon). A one-for- one type inventory policy is assumed at retailer node (lower echelon). Demands occurring during the stock out periods are assumed to be lost. The DC replenishes their stocks with exponential distributed lead times from warehouse (upper echelon) has abundant supply source. The items are supplied to the DC in packs of Q (= S-s) items from the warehouse. The steady state probability distribution and the operating characteristics are obtained explicitly. The required algorithm is derived and it is implemented using Mat lab. The measures of system performance in the steady state are obtained.

7-15

Authors: Titus J. O Aminer, Benard Okelo

In this paper, we examine conservative autonomous dynamic vibration equation, $\ddot{x}=-\tanh^{2}x$, which is time vibration of the displacement of a structure due to the internal forces, with no damping or external forcing. Numerical results using Wilson-theta method are tabulated and then represented graphically. Further the stability of the algorithms employed are also discussed.

27-33

Authors: Albert William, Roy Santiago, Indra Rajasingh

The packing chromatic number $\chi_{\rho}(G)$ of a graph $G$ is the smallest integer $k$ for which there exists a mapping $\pi:V(G)\longrightarrow \{1,2,...,k\}$ such that any two vertices of color $i$ are at distance at least $i+1$. It is a frequency assignment problem used in wireless networks, which is also called Broadcast coloring. It is proved that packing coloring is NP-complete for general graphs and even for trees. In this paper, we give the packing chromatic number for some classes of cycles.

51-60

Authors: Seenivasan Saravanakumar, K Nagarajan

Let G = (V;E) be a (p; q) - graph. A shortest path P is called a distant divisor path if l(P) divides q. Distance divisor graphD(G) of a graph G = (V;E) has the vertex set V = V (G) and two vertices in D(G) are adjacent if they have the distant divisor path in G. In this paper, we deal with distant divisor graph of subdivision of some graphs such as path, cycle, star and complete bipartite graph etc. Further we generalize the concept of antipodal graphs and prove that some distant divisor graphs are the generalized antipodal graphs. We also deal with the distant divisor graph of some graphs of diameter 4 and below.

67-72

Authors: D. K Thakkar, Dhaval Dinesh Kumar Pandya

In this paper we study the concept of edge critical graph with respect to total K domination and the characterization of edges whose deletion or addition are responsible for the decrement or increment in the total K domination number of a graph.

81-91

Authors: D. K Nathan, K Nagarajan

A subset cordial labeling of a graph G with vertex set $V$ is an injection $f$ from $V$ to the power set of$\{1, 2,\dots ,n\}$ such that an edge $uv$ is assigned the label $1$ if either $f(u)$ is a subset of $f(v)$ or $f(v)$ is a subset of $f(u)$ and $0$ otherwise. Then the number of edges labeled 0 and 1 differ by at most 1. If a graph has a subset cordial labeling then it is called a subset cordial graph. In this paper, we prove that some star related graphs such as splitting graph of star, identification of star with a graph are subset cordial.

103-111

Authors: Saima Nazeer, Imrana Kousar

Let $G$ be a connected graph with diameter diam$(G)$ and $d(x,y)$ denotes the distance between any two distinct vertices $x$, $y$ in $G$. A radio labeling $f$ of $G$ is an assignment of non negative integer to the vertices of $G$ satisfying $|f(x)-f(y)|\geq $diam$(G)-d(x,y)+1$. The span of a radio labeling is the maximum integer assigned to a vertex. The radio number of $G$ denoted by rn$(G)$, is the minimum possible span. In this paper, we determine the radio number for the prism related graphs, $D_{n}^{p}$ when $n=4k+2$.

119-128

Authors: K Lakshmiprabha, K Nagarajan

In this paper, we combine decomposition and domination and introduce the concept Ascending Domination Decomposition ($ADD$) of a graph $G$. 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 $\gamma(G_{i})=i$, $1\leqi\leq n$. In this paper, we prove $K_n$,$W_n$ and $K_{1,n}$ admit $ADD$. We also establish the characterization for the path and cycle that they should admit $ADD$. We also prove that the corona of path, cycle and star admit $ADD$.

139-144

Authors: U. P Acharya, Himali S. Mehta

The cartesian product of two graphs has been studied by many authors and has been generalized by introducing 2 - cartesian product G1 _2 G2 of two graphs G1 and G2. In this paper, we obtain G1 _2 G2; for Pn, Cn and Ks;t.

7-13

Authors: S K Vaidya, D. D. Bantva

An $L(2,1)$-labeling (or distance two labeling) of a graph $G$ is a function $f$ from the vertex set $V(G)$ to the set of nonnegative integers such that $|f(u)-f(v)|\geq2$ if $d(u,v)=1$ and $|f(u)-f(v)|\geq1$ if $d(u,v)=2$. The $L(2,1)$-labeling number $\lambda(G)$ of $G$ is the smallest number $k$ such that $G$ has an $L(2,1)$-labeling with max$\{f(v):v \in V(G)\}=k$. In this paper we find $\lambda$-number for some cacti.

21-32

Authors: Vipul Srivastava, Neha Mathur, Pankaj Mathur

Consider the trignometric polynomials $ r_{n}(x)=\frac{\cos (2n+1)\frac{\theta }{2}}{\cos \frac{\theta }{2}}$ and $s_{n}(x)=\frac{\sin (2n+1)\frac{\theta }{2}}{\sin \frac{\theta }{2}}.$ These polynomials are such that their zeros are interscaled and neither of the polynomials is the extrema of the other polynomial. On these interscaled set of nodes we study an interpolation process when Lagrange data is prescribed on one set of nodes and Hermite data is prescribed on the other set of nodes.

41-48

Authors: Mukkamala Sambasiva Rao, K P Shum

In this paper we introduce the notion of Boolean filters in a pseudo-complemented distributive lattice and characterize the class of all Boolean filters. Further a set of equivalent conditions are derived for a proper filter to become a prime Boolean filter. Also a set of equivalent conditions is derived for a pseudo-complemented distributive lattice to become a Boolean algebra. Finally, a Boolean filter is characterized in terms of congruences.

55-60

Authors: K Alli, A Subramanian, S Pious Missier

In this paper, we introduce g#p#- closed sets of a topological space and study their properties.

71-78

Authors: S Syed Ali Fathima, M Mariasingam

The authors introduced #rg-closed sets and #rg-open sets in topological spaces and established their relationships with some generalized sets in topological spaces. The aim of this paper is to introduce #rg-quotient maps using #rg-closed sets and characterize their basic properties.

85-91

Authors: J Krishnaveni, C Sekar

In this paper we study the soft semi separation of soft sets, soft semi connected sets and soft locally semi connected sets and prove some properties related to these topics.

107-114

Authors: P Vidhya, S Muthammai

Let $G = (V, E)$ be a nontrivial, simple, finite and undirected graph. A dominating set $D$ is called a complementary tree dominating set if the induced subgraph $$ is a tree. The minimum cardinality of a complementary tree dominating set is called the complementary tree domination number of $G$ and is denoted by $\gamma_{ctd}(G)$. A dominating set $D_t$ is called a total complementary tree dominating set if every vertex $v \in V$ is adjacent to an element of $D_t$ and $$ is a tree. The minimum cardinality of a total complementary tree dominating set is called the total complementary tree domination number of $G$ and is denoted by $\gamma_{tctd}$. In this paper, we determine the total complementary tree domination numbers of some grid graph.

129-140

Authors: Sanjay Jivrajbhai Ghevariya, Haresh V Dedania

Paul Wilmott derived BSM option pricing formula for the payoff function $\textrm{max}\{\textrm{ln}(\frac{S_T}{K}), 0\}$. In this article, we derive the BSM option pricing formula for the modified payoff function $\linebreak$ $\textrm{max}\{S_T \textrm{ln}(\frac{S_T}{K}), 0\}$. It turns out that the present BSM formula is quite close to the plain vanilla option pricing formula.

5-9

Authors: M. Valliammal, S. P. Subbiah, V. Swaminathan

Let $G=(V,E)$ be a graph without isolates. A subset $S$ of $V(G)$ is called a total dominating set of $G$ if for every $v\in V$, there exists $u\in S$ such that $u$ and $v$ are adjacent. $S$ is called a total complementary acyclic dominating set of $G$, if $S$ is a total dominating set of $G$ and $\left\langle V-S\right\rangle$ is acyclic. $V(G)$ is a total complementary acyclic dominating set of $G$ (since $G$ has no isolates). The minimum cardinality of a total complementary acyclic dominating set of $G$ is called the total complementary acyclic domination number of $G$ and is denoted by $\gamma_{c-a}^{t}(G)$. In this paper, characterization of graphs for which $\gamma_{c-a}^{t}(G)$ takes specific values are found.

17-20

Authors: S. Balamurugan, G. Prabakaran

A dominating set D of graph G = (V, E) is a disconnected dominating set, if the induced subgraph < D > is disconnected. The disconnected dominating number (G) of G is the minimum cardinality of a disconnected dominating set of G. In this paper, we relate this parameter to other parameters of graph G and obtain some bounds also. dc 

27-35

Authors: R. B. Gnana Jothi, A. Uma Devi

A graph G = (V, E) is said to be topogenic if it admits a topogenic set indexer, which is a set indexer f: V 2X such that f(V) is a topology on X. A list colouring of a graph G = (V,E) with a colour list C = for V = {v1, v2, ….vn} is a proper colouring of V by element of so that the adjacent vertices u,v are coloured differently and the colour for is in C(V). L- edge colouring of a graph G is an assignment L:E(G)2X- such that no two adjacent edges receive the same label where X is a ground set. A graph G is to be L- edge colourable if there exists an L- edge colouring of G. A comparative study of topogenic graphs and L- edge colourable graphs has been made in this paper.

41-48

Authors: N. Meena, A. Subramanian, V. Swaminathan

A subset S of V(G) of a graph G is called a strong (weak) efficient dominating set of G if for every v ∈ V(G), │Ns[v]∩S│= 1 (│Nw[v]∩S│= 1 ) where Ns(v) = { u ∈ V(G) : uv ∈ E(G), deg(u) ≥ deg(v) } and Nw(v) = { u ∈ V(G) : uv ∈ E(G), deg(v) ≥ deg(u)}, Ns[v] = Ns(v) ∪ {v}, Nw[v] = Nw(v) ∪ {v}. The minimum cardinality of a strong (weak) efficient dominating set is called strong (weak) efficient domination number of G and is denoted by γse (G) (γwe (G)). A graph G is strong efficient if there exists a strong efficient dominating set.

21-27

Authors: M.K. Siddiqui, A. Ahmad, M.F. Nadeem, Y. Bashir

An edge irregular total $k$-labeling $\varphi: V\cup E \to \{ 1,2, \dots, k \}$ of a~graph $G=(V,E)$ is a~labeling of vertices and edges of $G$ in such a~way that for any different edges $uv$ and $u'v'$ their weights $\varphi(u)+ \varphi(uv) + \varphi(v)$ and $\varphi(u')+ \varphi(u'v') + \varphi(v')$ are distinct. The total edge irregularity strength, $tes(G)$, is defined as the minimum $k$ for which $G$ has an~edge irregular total $k$-labeling. In this paper, we consider the total edge irregularity strength of the disjoint union of $\emph{p}$ isomorphic sun graphs, $tes(\emph{p}M_{n})$, disjoint union of $\emph{p}$ consecutive non-isomorphic sun graphs, $tes(\bigcup_{j=1}^{\emph{p}}M_{n_{j}})$.

37-46

Authors: B. Sakthi @ Sathya, S. Murugesan

In this paper, we introduce a new classes of sets namely rpsI- closed sets in ideal topological spaces and investigate their properties and relations.

53-59

Authors: N. B. Okelo, J. O. Agure, P. O. Oleche

Let H be an infinite dimensional complex Hilbert space and B(H) the algebra of all bounded linear operators on H. In this paper, we study norm-attainability for elementary operators and generalized derivations. We give results on necessary and sufficient conditions for norm-attainability.

69-78

Authors: R. Sridevi, K. Krishnaveni, S. Navaneethakrishnan

In this paper, we propose a novel watershed image segmentation technique based on absolute difference graph labeling. The main objective is to partition the image into distinct regions that are visually different, homogeneous and meaningful with respect to some characteristics or computed property, that is, such as grey level, texture or color to enable easy image analysis. A graph representing an image is derived from the similarity between the pixels and partitioned by a computationally efficient absolute difference graph method, which identifies representative vertices for each absolute difference and then expands them to obtain complete absolute difference graph labeling. As a result, the image is portioned into a set of disjoint labels (regions).

87-96

Authors: J. Sunday, M.R. Odekunle, A.O. Adesanya

In this research work, we present the derivation and implementation of an order six block integrator for the solution of first-order ordinary differential equations using interpolation and collocation procedures. The approximate solution used in this work is a combination of power series and exponential function. We further investigate the properties of the block integrator and found it to be zero-stable, consistent and convergent. The block integrator is further tested on some real-life numerical problems and found to be computationally reliable.