Intersection graph of gamma sets in the total graph

Abstract

In this paper, we consider the intersection graph I (Z n ) of gamma sets in the total graph on Z n . We characterize the values of n for which I (Z n ) is complete, bipartite, cycle, chordal and planar. Further, we prove that I (Z n ) is an Eulerian, Hamiltonian and as well as a pancyclic graph. Also we obtain the value of the independent number, the clique number, the chromatic number, the connectivity and some domination parameters of I (Z n ).