Edge-three Cordial Graphs Arising from Complete Graphs

Abstract

A graph $G$ is said to be $E_k$-Cordial if there is an edge labeling $f:E(G)\to \{0,1,\dots ,k-1\}$ such that, at each vertex $v$, the sum modulo $k$ of the labels on the edges incident with $v$ is $f(v)$ and it satisfies the inequalities $|v_f(i)–v_f(j)|\le 1$ and $|e_f(i)–e_f(j)|\le 1$, where $v_f(s)$ and $e_f(t)$ are, respectively, the number of vertices labeled with $s$ and the number of edges labeled with $t$. The map $f$ is then called an $E_k$-cordial labeling of $G$.

This paper investigates $E_3$-cordiality of snakes, one point unions, path unions, and coronas involving complete graphs.