Certain findings on the gamma graph of some graphs

Abstract

Suppose every vertex v ???? V in graph G is either an element of subset S or is close to an element of subset S. In that case, subset S is said to be a dominant set of the vertex set V. If a set S is a γ-set. Its minimal cardinality is equal to the dominance number γ(G) of G. Any two vertices in a graph G are considered neighboring if their γ-sets vary by precisely one vertex. The gamma graph of G is denoted as γ · G, and its γ-sets serve as vertices in the graph. We discuss the gamma graph of path, cycle, ladder, and star graphs in the middle of the paper and look at a number of results pertaining to the gamma graph of pan and lollipop graphs.