A Note on Separation Number of Graphs
A. R. Latheesh Kumar *
Department of Mathematics, St. Mary’s College Sulthan Bathery, Wayanad, Kerala, 673 592, India.
*Author to whom correspondence should be addressed.
Abstract
In this paper, the concept of total domination is used to introduce a new graph parameter, called the separation number Sn(G) of a graph G. We study the fundamental properties of this parameter and establish general lower and upper bounds for Sn(G). Furthermore, the separation number is determined for various classes of graphs, including complete graphs and star graphs. We also examine the behavior of Sn(G) under specific graph operations such as the corona of graphs and the conormal product of complete graphs.
Keywords: Total domination set, separation number, complete graphs, star graphs