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.