On the First Zagreb Index of Neighborhood Corona Graphs

Abstract

The first Zagreb index is defined as the sum of squares of the degrees of vertices in a graph. The neighborhood corona, G*H, of two graphs is defined as the graph obtained by taking one copy of G and vertical bar V (G)vertical bar copies of H and for each i, making all vertices in the ith copy of H adjacent with the neighbors of v(i), i = 1, 2, ... , vertical bar V (G)vertical bar. In this paper, the first Zagreb index of neighborhood corona graphs is computed, and exact formulas are derived.