The present note is devoted to establish some extremal results for the zeroth-order general Randi'{c} index of cacti, characterize the extremal polyomino chains with respect to the aforementioned index, and hence to generalize two already reported results.

Recently two new degree concepts have been defined in graph theory: ev-degree and ve-degree. Also the evdegree and ve-degree Zagreb and Randić indices have been defined very recently as parallel of the classical definitions of Zagreb and Randić indices. It was shown that ev-degree and ve-degree topological indices can be used as possible tools in QSPR researches . In this paper we d...

Let G be an undirected simple graph with n vertices and m edges. Denote with |λ1| |λ2| · · · |λn| and |ρ1| |ρ2| · · · |ρn| absolute eigenvalues and Randić eigenvalues of G arranged in non-increasing order, respectively. Upper bound of graph invariant E(G) = ∑i=1 |λi| , and lower and upper bounds of invariant RE(G) =∑i=1 |ρi| are obtained in this paper.

Wiener index is a topological index based on distance between every pair of vertices in a graph G. It was introduced in 1947 by one of the pioneer of this area e.g, Harold Wiener. In the present paper, by using a new method introduced by klavžar we compute the Wiener and Szeged indices of some nanostar dendrimers.

A topological index is a numeric quantity assigned to graph that characterizes the structure of graph. Topological indices and physico-chemical properties such as atom-bond connectivity ABC , Randić, geometric-arithmetic id="M2"> GA</mtext...

The Randić index of a graph G, written R(G), is the sum of 1 √ d(u)d(v) over all edges uv in E(G). Let d and D be positive integers d < D. In this paper, we prove that if G is a graph with minimum degree d and maximum degree D, then R(G) ≥ √ dD d+Dn; equality holds only when G is an n-vertex (d,D)-biregular. Furthermore, we show that if G is an n-vertex connected graph with minimum degree d and...

Let G be a (molecular) graph with vertex set V 1⁄4 fv1;v2; . . . ;vng. Let dðv iÞ be the degree of the vertex v i 2 V . If the vertices v i1 ;v i2 ; . . . ;v ihþ1 form a path of length h;h P 1, in the graph G, then the hth order Randić index Rh of G is defined as the sum of the terms 1= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffif...