Independent differential in graphs

Abstract

Let  be a graph of order  and let  be the set of vertices in  that have a neighbor in the vertex set . The independent differential of an independent vertex set  is defined as  and the maximum value of  for any independent subset  of is the independent differential of . An independent set  of vertices of a graph  is said to be an independent dominating set if every vertex in  is adjacent to a vertex in .  is an independent dominant differential graph if it contains a -set which is also an independent dominating set. In this paper, the study on properties of  is initiated and some upper and lower bounds on  are presented. This paper is devoted to the computation of independent differential of wheel, cycle, path-related graphs, and graph operations. Furthermore, independent dominant differential graph types are recognized.