Topological Indices of Mycielkian graph

Abstract: There are many topological indices. Among the degree based topological indices, Randic index Zagreb indices, Banhatti indices, Atom bond connectivity index, Harmonic index, Geometric arithmetic index and Revan vertex degree index etc. For a given graph GV,E of order n with vertex set   1 2 3 , , ,..., n V  v v v v . The Mycielski graph of G, denoted by M G , is the graph with vertex set   1 V V  u , where   1 1/ i i V  v v V and edge set     1 1 1 1 / / i j i j i i E v v v v E  v u v V . The vertex 1 i v is called the copy of the vertex i v and u is called the root of M G . In this paper we obtain Randic index, Zegreb index, Atom Bond Connectivity index, Harmonic index, Augmented Zagreb index, Sum Connectivity index, geometric arithmetic index and Revan index of Myceilskian graph.