The first and second Zagreb indices, since its inception have been subjected to an extensive research in the physio- chemical analysis of compounds. In [6] Hanyuan Deng et.al computed indices four new operations on a graph defined by M. Eliasi, B. Taeri [4]. Motivated from this we define operation graphs compute resultant graph. We illustrate results with some examples.

Many existing degree based topological indices can be clasified as bond incident degree (BID) indices, whose general form is BID(G) = ∑ uv∈E(G) Ψ(du, dv), where uv is the edge connecting the vertices u, v of the graph G, E(G) is the edge set of G, du is the degree of the vertex u and Ψ is a non-negative real valued (symmetric) function of du and dv. Here, it has been proven that if the extensio...

We obtain inequalities involving many topological indices in classical graph products by using the f-polynomial. In particular, we work with lexicographic product, Cartesian sum and first Zagreb, forgotten, inverse degree lordeg indices.

In this paper, we present sharp bounds for the Zagreb indices, Harary index and hyperWiener index of graphs with a given matching number, and we also completely determine the extremal graphs. © 2010 Elsevier Ltd. All rights reserved.