SECURE MONOPHONIC DOMINATION NUMBER OF PRODUCT OF GRAPHS

SECURE MONOPHONIC DOMINATION NUMBER OF PRODUCT OF GRAPHS

K. Sunitha, D. Josephine Divya

[PDF]

Abstract

Let G be a graph which is connected. A monophonic dominating set M is said to be a secure monophonic dominating set Sm(written as SMD set) of G if for each g ∈ V \M there exists f ∈ M such that g is adjacent to f and Sm = (M\{f} ∪ {g} is a monophonic dominating set. The smallest cardinality of a secure monophonic dominating set of G is the secure monophonic domination number of G and the notation is γsm(G). In this article, we discuss the secure monophonic domination number of product of graphs.

Keywords

Monophonic path, Monophonic domination number, Secure monophonic domination number, Cartesian product and Corona product.