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.