Abstract
In this paper, we present some new lower and upper bounds for the modified Randic index in terms of maximum, minimum degree, girth, algebraic connectivity, diameter and average distance. Also we obtained relations between this index with Harmonic and Atom-bond connectivity indices. Finally, as an application we computed this index for some classes of nano-structures and linear chains.
Highlights
In this paper is a simple connected graph, where is the set vertex of, and is the edge set of
There are many different kinds of chemical indices that some of them are distance based like Wiener index, some of them are based on degree like Randic index
The Randic index was proposed by Milan Randic in 1975
Summary
In this paper is a simple connected graph, where is the set vertex of , and is the edge set of. The Randic index was proposed by Milan Randic in 1975 This topological index was named Branching index, later called Randic index, which defined as where denote the degree of vertex. This index has been defined to measure the extent of branching of the carbon-atom skeleton of saturated hydrocarbons. Let be the average distance of G that defined as such that is the Wiener index defined as the sum of the lengths of the shortest path between all pairs of vertices and diameter of is the maximum distance over all pairs of vertices and of denoted by between Randic index and diameter of a graph. We obtain a new bounds for the modified Randic index in terms of girth, diameter and algebraic connectivity. For more information about harmonic and ABC index we refer the reader to see [7,11,26,29]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
