Counting relations for general zagreb indices

Abstract

The first and second general Zagreb indices of a graph G, with vertex set V and edge set E, are defined asMk1 = ∑v∈V d(u)k and Mk2 = ∑uv∈E[d(u) d(v)]k, where d(v) is the degree of the vertex v of G. We present combinatorial identities, relating Mk1 and Mk2 with counts of various subgraphs contained in the graph G.