A Note on Separation Number of Graphs

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.