E-cordial Labeling for Cartesian Product of Some Graphs

We investigate E-cordial labeling for some cartesian product of graphs. We prove that the graphs Kn × P2 and Pn × P2 are E-cordial for n even while Wn × P2 andK1,n × P2 are E-cordial for n odd. Key words: E-Cordial labeling; Edge graceful labeling; Cartesian produc

A Study on Graph Theory of Path Graphs

A simple graph G = (V, E) consists of V , a nonempty set of vertices, and E, a set of unordered pairs of distinct elements of V called edges. Simple graphs have their limits in modeling the real world. Instead, we use multigraphs, which consist of vertices and undirected edges between these vertices, with multiple edges between pairs of vertices allowed. In the mathematical field of graph theory, a path graph or linear graph is a graph whose vertices can be listed in the order v1, v2, …, vn such that the edges are {vi, vi+1} where i = 1, 2, …, n ? 1. Equivalently, a path with at least two vertices is connected and has two terminal vertices (vertices that have degree 1), while all others (if any) have degree 2. Paths are often important in their role as subgraphs of other graphs, in which case they are called paths in that graph. A path is a particularly simple example of a tree, and in fact the paths are exactly the trees in which no vertex has degree 3 or more. A disjoint union of paths is called a linear forest

Group Irregular Labelings of Disconnected Graphs

We investigate the \textit{group irregularity strength} ($s_g(G)$) of graphs, i.e. the smallest value of $s$ such that taking any Abelian group \gr of order $s$, there exists a function f:E(G)\rightarrow \gr such that the sums of edge labels at every vertex are distinct. We give the exact values and bounds on $s_g(G)$ for chosen families of disconnected graphs. In addition we present some results for the \textit{modular edge gracefulness} $k(G)$, i.e. the smallest value of $s$ such that there exists a function f:E(G)\rightarrow \zet_s such that the sums of edge labels at every vertex are distinct

Fibonacci and Super Fibonacci Graceful Labeling of Some Graphs

Abstract: In the present work we discuss the existence and non-existence of Fibonacci and super Fibonacci graceful labeling for certain graphs. We also show that the graph obtained by switching a vertex in cycle Cn, (where n >= 6 ) is not super Fibonacci graceful but it can be embedded as an induced subgraph of a super Fibonacci graceful graph. Key words: Graceful Labeling; Fibonacci Graceful Labeling; Super Fibonacci Graceful Labelin