On the total product cordial labeling on the cartesian product of $P_{m} imes C_{n}$, $C_{m} imes C_{n}$ and the generalized Petersen graph $P(m,n)$

On the total product cordial labeling on the cartesian product of $P_{m} imes C_{n}$, $C_{m} imes C_{n}$ and the generalized Petersen graph $P(m,n)$

**Authors : **

Ariel C. Pedrano ^{a,∗} and Ricky F. Rulete ^{b}

**Author Address : **

^{a,b} Department of Mathematics and Statistics, College of Arts and Sciences, University of Southeastern Philippines, Davao City, Philippines.

*Corresponding author.

**Abstract : **

A total product cordial labeling of a graph $G$ is a function $f:V o {0,1}$. 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 the cartesian product of $P_{m} imes C_{n}$, $C_{m} imes C_{n}$ and the generalized Petersen graph $P(m,n)$.

**Keywords : **

Graph Labeling, Total Product Cordial Labeling.

**Article Info : **

*Received : * January 19, 2017; *Accepted : * June 03, 2017.