Properties of disjunctive domination in product graphs
Authors :
A. Lekha 1 * and K.S. Parvathy 2
Author Address :
1,2 Research Department of Mathematics, St. Mary’s College, Thrissur-680020, Kerala, India.
*Corresponding author.
Abstract :
In this paper properties of disjunctive domination in some graph products are studied. We examine whether disjunctive domination number is multiplicative with respect to different graph products, that is, $\gamma_2^d(G_1\ast G_2) \geq \gamma_2^d(G_1)\gamma_2^d(G_2)$ for all graphs $G_1$ and $G_2$ or $\gamma_2^d(G_1\ast G_2) \leq \gamma_2^d(G_1)\gamma_2^d(G_2)$ for all graphs $G_1$ and $G_2$ where $\ast$ denotes lexicographic, tensor, strong or Cartesian product of graphs. Some other inequalities involving disjunctive domination number of product graphs and the graphs attaining these inequalities are also given.
Keywords :
Domination, disjunctive domination, disjunctive domination number, graph product.
DOI :
Article Info :
Received : October 13, 2019; Accepted : December 27, 2019.
