Zagreb indices of graphs

摘要

The first Zagreb index M_1 (G) is equal to the sum of squares of the degrees of the vertices, and the second Zagreb index M_2(G) is equal to the sum of the products of the degrees of pairs of adjacent vertices of the underlying molecular graph G. In this paper, we obtain lower and upper bounds on the first Zagreb index M_1 (G) of G in terms of the number of vertices (n), number of edges (m), maximum vertex degree (A), and minimum vertex degree (5). Using this result, we find lower and upper bounds on M_2(G). Also, we present lower and upper bounds on M_2(G) + M_2(G-bar) in terms of n, m, A, and S, where G denotes the complement of G. Moreover, we determine the bounds on first Zagreb coindex M-bar_1{G) and second Zagreb coindex M-bar_2(G). Finally, we give a relation between the first Zagreb index and the second Zagreb index of graph G.