International Journal of Mathematics and Soft Computing

1-5

Authors: M Ramakrishnan, Sowmya Swaminathan, Jayaganesan Chandresekaran

In order to achieve resilient multipath routing with efficient path choosing dynamically, we introduce the concept of Weighted Independent Directed Acyclic Graphs (WIDAGs). In a given network we develop polynomial-time algorithms to compute link-independent and node-independent DAGs. We use Heuristic methods to dynamically choose the maximum profitable (least cost) route upon a single link failure. The algorithm developed in this paper takes the advantage of the resiliency provided by IDAG and in addition, improves efficiency by choosing least cost path dynamically.

15-19

Authors: Akbar Zada, Gul Rahmat, Afshan Tabassum, Gohar Ali

Let $\mathbb{T}=\{T(n)\}_{n\geq 0}$ be a discrete semigroup of bounded linear operators acting on a Banach space $X$. We prove that if for each $\mu \in \mathbb{R}$ and every $q$-periodic sequence $f$ with $f(0)=0$, the sequence $n\rightarrow \sum_{k=0}^{n}e^{i\mu k}T(n-k)f(k)$ is bounded, then the semigroup$\mathbb{T}$ is uniformly exponentially stable.

33-39

Authors: R Sridevi, K Nagarajan, A Nellaimurugan, S Navanaeethakrishnan

Let $G=(V,E)$ be a $(p,q)$-graph. A Fibonacci divisor cordial labeling of a graph G with vertex set V is a bijection $f : V \rightarrow \{F_1, F_2,F_3,\dots ,F_p\}$, where $F_i$ is the $i^{th}$ Fibonacci number such that if each edge $uv$ is assigned the label $1$ if $f(u)$ divides $f(v)$ or $f(v)$ divides $f(u)$ 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 Fibonacci divisor cordial labeling, then it is called Fibonacci divisor cordial graph. In this paper, we prove that the graphs $P_n$, $C_n$, $K_{2,n} \odot u_2(K_1)$ and subdivision of bistar(\textless $B_ {n,n}:w>)$ are Fibonacci divisor cordial graphs. We also prove that $K_n(n\geq 3)$ is not Fibonacci divisor cordial graph.

49-53

Authors: S K Vaidya, C M Barasara

For a graph $G=(V(G), E(G))$, a function $ f : E(G) \rightarrow \{0, 1\}$ is called an edge product cordial labeling of $G$ if the induced vertex labeling function defined by the product of incident edge labels be such that the edges with label 1 and label 0 differ by at most 1 and the vertices with label 1 and label 0 also differ by at most 1. In this paper we investigate some new families of edge product cordial graph.

61-70

Authors: V L Stella Arputha Mary, S Navaneethakrishnan, A Nagarajan

For any non-trivial abelian group $A$ under addition a graph $G$ is said to be $A-$ magic if there exists a labeling $f$ of the edges of $G$ with non zero elements of $A$ such that, the vertex labeling $f^+$ defined as $f^+(v)= \Sigma f(uv)$ taken over all edges $uv$ incident at $v$ is a constant \cite {rm}. A graph is said to be $A$-magic if it admits an $A$-magic labeling. In this paper we prove that splitting graph of a path, triangular snake and book graphs are $Z_4$-magic graphs. Also we generalize that they are all $Z_{4p}$-magic graphs for any positive integer $p$.

79-83

Authors: I Sahul Hamid, S Balamurugan

A subset $D$ of the vertex set $V(G)$ of a graph $G$ is called a dominating set of $G$ if every vertex in $V-D$ is adjacent to a vertex in $D$. A dominating set $D$ such that $$ has an isolated vertex is called an isolate dominating set and the minimum cardinality of an isolate dominating set is called the isolate domination number of $G$ and is denoted by $\gamma_0(G)$. In this paper we characterize the unicyclic graphs in which the order equals the sum of the isolate domination number and its maximum degree.

93-105

Authors: Lakshmi Alias Gomathi, A Nagarajan, A Nellaimurugan

A simple graph G is called near felicitous if there exists a 1 – 1 function f:V(G) → {0, 1, 2, . . . , q – 1, q + 1} such that the set of induced edge labels f *(uv) = (f(u) + f(v)) (mod q) are all distinct when the addition is taken modulo q with residues 1, 2, 3, . . . , q. It is shown that an even subgraph of a near felicitous graph with an even number of edges contain an even number of odd labeled edges. As a consequence, some families of graphs are shown to be non – near felicitous.

115-128

Authors: Joseph W Wilder

The use of mathematics and computers in the generation of art is an ever growing field. This work concerns the development of an algorithm based on the solution of a partial differential equation that can be used with digital images to generate art-like drawings. This modified model uses a conceptual framework that includes local and global perspectives to determine which aspects of the objects in the image should be included in the drawing. This novel inclusion of both of these perspectives results in drawings with enhanced art-like qualities compared with those utilizing a single perspective.

1-4

Authors: M. Kalanithi, V. Swaminathan A. Selvam

In this paper the extremal graphs on the domination number of the distance $k$-complement graph $G_k^c$ of a graph $G$ are characterized and the relation between the domination number of $G_k^c$ and the distance $k$-domination number of $G$ are established.

11-15

Authors: Mathavi Manisekar, S. Lalitha

Amino acids, the monomer units of protein, play an important role in all biological species. Two amino acids combine by the elimination of a molecule of water to produce a dipeptide and the linkage is known as peptide link or peptide bond. Chemical graphs serve as a convenient model of any real or abstract chemical system. The energy of a chemical graph is the sum of the absolute eigen values of the adjacency matrix of the graph. The aim of this work is to make a theoretical estimation of the energies of graphs associated with the amino acids constituting the dipeptide and that of the peptide itself. It is found that the energy during the formation of dipeptide is conserved for various di-peptides.

21-25

Authors: P. Jayapraksah, V. Swaminathan

Let G = (V, E) be a simple graph. A clique of G is a maximal complete subgraph of G. A subset D of V which meets every clique of G is called a clique transversal set of G. Since V(G) is a clique transversal set of G, the existence of a clique transversal set of G is guaranteed in any graph. The minimum cardinality of a clique transversal set of G is called the clique transversal number of G and is denoted by rclt(G). A study on this concept is initiated in this paper.

37-40

Authors: R.B. Gnana Jothi, R. Ezhil Mary

In a graph structure G = (V, E1, E2… Ek), the capacity of a vertex c(v) is the number of different Ei edges incident at v. In this paper, we have made an attempt to answer the problem of examining the graph structures for which sum of vertex capacities is equal to sum of number of relations and the number of edges in the structure for some families of graphs viewed as graph structures.

49-58

Authors: P. Jeyanthi, G. Hemalatha

In this paper we determine the total restrained dominating set and the total restrained domination subdivision number for Cartesian product graph.

13-20

Authors: S K Vaidya, U M Prajapati

In this paper, we investigate prime labeling for some graphs obtained by duplication of graph elements and also we derive some result for Pn, K1,n and Cn in this context.

29-35

Authors: M. Sambasiva Rao

The notion of multipliers is introduced in a hypersemilattice and some properties of multipliers are studied. In addition, a set of equivalent conditions are established for two multipliers of a hypersemilattice to be equal in the sense of mappings. Further, the properties of invariance subsets and invariance congruences are studied with respect to multipliers.

47-51

Authors: J. Joseline Manora, V. Swaminathan

This paper deals the graphs for which the removal of any vertex changes the majority domination number of the graph. In the following section, how the removal of a single vertex from $G$ can change the majority domination number is surveyed for trees. Characterisation of $V^+_M(G)$ ~and~ $V^-_M(G)$ are determined.

61-68

Authors: S K Vaidya, N H Shah

In this paper, we prove that the square graph of bistar Bn,n, the splitting graph of Bn,n and the splitting graph of star K1,n are graceful graphs. We also prove that the splitting graph and the shadow graph of bistar Bn,n admit odd graceful labeling.

79-86

Authors: Kishore Kumar, Srivastava, Jitendra Kumar, Nity Srivastava

The self-similar solutions for point source magnetoradiative exponential shock wave moving into uniform atmosphere of dusty gas where total energy of wave depend on cube of shock radius has discussed. The effects of radiation on the discontinuities are also investigated. The ordinary differential equation obtained by similarity method are solved by software Matlab. The nature of flow variables are illustrated through graphs.

97-105

Authors: V. Lakshmi alias Gomathi, A. Nagarajan, A. Nellai Murugan

A simple graph G is called felicitous if there exists a one-to-one function f : V(G) → {0,1,2, . . . , q} such that the set of induced edge labels f *(uv) = (f(u) + f(v)) (mod q) are all distinct. In this paper we show that Pr,2m+1, Pr2m+1 and Cn x Pm are felicitous graphs