Zagreb indices and coindices of product graphs

Abstract

For a (molecular) graph, the first Zagreb index M1M1 is equal to the sum of squares of the degrees of vertices, and the second Zagreb index M2M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. Similarly, the first and second Zagreb coindices are defined as ¯¯¯¯¯¯M1(G)=∑uv∉E(G)(dG(u)+dG(v))M¯1(G)=∑uv∉E(G)(dG(u)+dG(v)) and ¯¯¯¯¯¯M2(G)=∑uv∉E(G)dG(u)dG(v)M¯2(G)=∑uv∉E(G)dG(u)dG(v). In this paper, we compute the Zagreb indices and coindices of strong, tensor and edge corona product of two connected graphs. We apply some of our results to compute the Zagreb indices and coindices of open and closed fence graphs.