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.

We introduce reflexive polytopes of index l as a natural generalisation of the notion of a reflexive polytope of index 1. These l-reflexive polytopes also appear as dual pairs. In dimension two we show that they arise from reflexive polygons via a change of the underlying lattice. This allows us to efficiently classify all isomorphism classes of l-reflexive polygons up to index 200. As another ...

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...

Let M be a smooth closed spin manifold. The higher index theorem computes the pairing between the group cohomology of π1(M) and the Chern character of the “higher” index of a Dirac-type operator on M. Using superconnections, we give a heat equation proof of this theorem on the level of differential forms on a noncommutative base space. As a consequence, we obtain a new proof of the Novikov conj...