Further Results on 3-Difference Cordial Graphs

Abstract

Let $G$ be a $(p,q)$ graph. Let $f:V(G)\to \{1,2,\dots ,k\}$ be a map where $k$ is an integer $2\le k\le p$. For each edge $uv$, assign the label $|f(u)–f(v)|$. $f$ is called $k$-difference cordial labeling of $G$ if $|v_f(i)–v_f(j)|\le 1$ and $|e_f(0)–e_f(1)|\le 1$, where $v_f(x)$ denotes the number of vertices labeled with $x$, $e_f(1)$ and $e_f(0)$ respectively denote the number of edges labeled with 1 and not labeled with 1. A graph with a $k$-difference cordial labeling is called a $k$-difference cordial graph. In this paper, we investigate 3-difference cordial labeling behavior of slanting ladder, book with triangular pages, middle graph of a path, shadow graph of a path, triangular ladder, and the armed crown.