Edge Difference Cordial Labeling of Graphs

Abstract

We put up a dissimilar of difference cordial labeling namely as edge difference cordial labeling. As interchange the roles of vertices and edges in difference cordial labeling. Let $G$ be a $(p,q)$ graph. Let $k$ be an integer with $1\leq k\leq q$ and $f:E(G)\rightarrow \{1,2,\ldots, k\}$ be a map. For each vertex $v$, assign the label $\min|(f(e_i)-f(e_j))|$. The function $f$ is called an edge difference cordial labeling of $G$ if $f$ is one-to-one map and $|v_{f}(1)-v_{f}(0)|\leq1$ where $v_{f}(x)$ denotes the number of vertices labeled with $x \ (x\in\{1,2,\ldots,k\})$, $e_{f}(1)$ and $e_{f}(0)$ respectively denote the number of edges labeled with 1 and not labeled with 1. A graph with an edge difference cordial labeling is called an edge difference cordial graph. In this paper we investigate some results on newly defined idea.