On Total Product Cordial Labeling of Some Crown Graphs

Abstract

A total product cordial labeling of a graph $G$ is a function $f:V \to \{0,1\}$. For each $xy$, assign the label $f(x)f(y)$, $f$ is called total product cordial labeling of $G$ if it satisfies the condition that $|v_{f}(0)+e_{f}(0)-v_{f}(1)-e_{f}(1)|\leq 1$ where $v_{f}(i)$ and $e_{f}(i)$ denote the set of vertices and edges which are labeled with $i=0,1$, respectively. A graph with a total product cordial labeling defined on it is called total product cordial. In this paper, we determined the total product cordial labeling of $P_{m} \circ C_{n}$, $P_{m} \circ P_{n}$, $C_{m} \circ P_{n}$, $P_{m} \circ F_{n}$, $P_{m} \circ W_{n}$ and $P_{m} \circ K_{n}$.