$E$-cordial Graphs

Abstract

A graph $G=(V,E)$ is called $E$-cordial if it is possible to label the edges with the numbers from the set $N=\{0,1\}$ and the induced vertex labels $f(v)$ are computed by $f(v)=\sum _{\mathrm{\forall }u}f(u,v)(\mathrm{mod}2)$, where $v\in V$ and $\{u,v\}\in E$, so that the conditions $|v_f(0)|–|v_f(1)|\le 1$ and $||e_f(0)|–|e_f(1)|\le 1$ are satisfied, where $|v_f(i)|$ and $|e_f(i)|$, $i=0,1$, denote the number of vertices and edges labeled with $0$’s and $1$’s, respectively. The graph $G$ is called $E$-cordial if it admits an $E$-cordial labeling. In this paper, we investigate $E$-cordiality of several families of graphs, such as complete bipartite graphs, complete graphs, wheels, etc.