Journal of Discrete Mathematics

Volume 2013 (2013), Article ID 892839, 9 pages

http://dx.doi.org/10.1155/2013/892839

## Induced Graphoidal Decompositions in Product Graphs

^{1}Department of Mathematics, Christ University, Bangalore, Karnataka 560029, India^{2}Department of Mathematics, The Madura College, Madurai, Tamil Nadu 625011, India

Received 25 July 2012; Revised 20 October 2012; Accepted 5 November 2012

Academic Editor: Annalisa De Bonis

Copyright © 2013 Mayamma Joseph and I. Sahul Hamid. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Let be a nontrivial, simple, finite, connected, and undirected graph. A graphoidal decomposition (GD) of is a collection of nontrivial paths and cycles in that are internally disjoint such that every edge of lies in exactly one member of . By restricting the members of a GD to be induced, the concept of induced graphoidal decomposition (IGD) of a graph has been defined. The minimum cardinality of an IGD of a graph is called the induced graphoidal decomposition number and is denoted by (). An IGD of without any cycles is called an induced acyclic graphoidal decomposition (IAGD) of , and the minimum cardinality of an IAGD of is called the induced acyclic graphoidal decomposition number of , denoted by (). In this paper we determine the value of () and () when is a product graph, the factors being paths/cycles.