Total Domination Number of Kronecker Product of Wheel Graphs

Abstract

The paper is related on the analytical study of total domination number of Kronecker product of Wheel Graph. Cockayne, Dawes and Hedetniemi introduced the total domination in graphs. In this paper, first we have defined the Kronecker product of wheel graph  for  . Then, we will find the exact value of total domination number of Kronecker product of Wheel Graphs in generalize form. If  and  are two graphs with their vertex set  and respectively then the Kronecker product of these two graphs is defined to be a graph with its vertex set as  such that  is the Cartesian product of the sets  and . Where two vertices in Kronecker product graph have an edge if and only if  and  are edges in graph  and  respectively.