On the total product cordial labeling on the cartesian product of $P_m \times C_n$, $C_m \times C_n$ and the generalized Petersen graph $P(m, n)$

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DOI:

https://doi.org/10.26637/mjm503/007

Abstract

A total product cordial labeling of a graph $G$ is a function $f: V \rightarrow\{0,1\}$. For each $x y$, assign the label $f(x) f(y), f$ is called total product cordial labeling of $G$ if it satisfies the condition that $\mid v_f(0)+e_f(0)-$ $v_f(1)-e_f(1) \mid \leq 1$ 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 $P_m \times C_n, C_m \times C_n$ and the generalized Petersen graph $P(m, n)$.

Keywords:

Graph Labeling, Total Product Cordial Labeling

Mathematics Subject Classification:

Mathematics
  • Ariel C. Pedrano Department of Mathematics and Statistics, College of Arts and Sciences, University of Southeastern Philippines, Davao City, Philippines.
  • Ricky F. Rulete Department of Mathematics and Statistics, College of Arts and Sciences, University of Southeastern Philippines, Davao City, Philippines.
  • Pages: 531-539
  • Date Published: 01-07-2017
  • Vol. 5 No. 03 (2017): Malaya Journal of Matematik (MJM)

Cahit, I., "Cordial graphs: A weaker version of graceful and harmonious Graphs", Ars Combinatoria, 23 $(1987), 201-207$

Gallian, J. A., "A dynamic survey on graph labeling", The Electronic Journal of Combinatorics, Sixteenth Edition, (2013).

Sundaram, M., Ponraj, P. and Somasundaram, S., "Product cordial labeling of graphs", Bulletin of Pure and Applied Sciences, 23E (1) (2004), 155-162.

Sundaram, M., Ponraj, P. and Somasundaram, S., "Total Product Cordial Labeling of Graphs", Bulletin of Pure and Applied Sciences, 23E (1) (2005), 199-203.

West, D. B., An Introduction to Graph Theory, Prentice Hall, (1996).

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Published

01-07-2017

How to Cite

Ariel C. Pedrano, and Ricky F. Rulete. “On the Total Product Cordial Labeling on the Cartesian Product of $P_m \times C_n$, $C_m \times C_n$ and the Generalized Petersen Graph $P(m, n)$”. Malaya Journal of Matematik, vol. 5, no. 03, July 2017, pp. 531-9, doi:10.26637/mjm503/007.