We study eccentricity-based indices such as Zagreb eccentricity indices, general index and total index. present exact values of generalized networks related to binary $m$-ary trees, where $m \ge 2$.

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...

The chromatic number of a graph G, denoted by χ(G), is the minimum number of colors such that G can be colored with these colors in such a way that no two adjacent vertices have the same color. A clique in a graph is a set of mutually adjacent vertices. The maximum size of a clique in a graph G is called the clique number of G. The Turán graph Tn(k) is a complete k-partite graph whose partition...