The index of a signed graph is the largest eigenvalue its adjacency matrix. For positive integers n and m ? 2 / 4 , we determine maximum complete graphs with vertices negative edges characterize achieving this maximum. This settles (the corrected version of) conjecture by Koledin Stani? (2017).

Abstract We consider two recent conjectures made by Harrington, Henninger-Voss, Karhadkar, Robinson and Wong concerning relationships between the sum index, difference index exclusive number of graphs. One conjecture posits an exact relationship first invariants; we show that in fact predicted value may be arbitrarily far from truth either direction. In process establish some new bounds on both...

A {it topological index} of a graph is a real number related to the graph; it does not depend on labeling or pictorial representation of a graph. In this paper, we present the upper bounds for the product version of reciprocal degree distance of the tensor product, join and strong product of two graphs in terms of other graph invariants including the Harary index and Zagreb indices.

Let G be a simple graph with vertex set V(G) {v1,v2 ,...vn} . For every vertex i v , ( ) i  v represents the degree of vertex i v . The h-th order of Randić index, h R is defined as the sum of terms 1 2 1 1 ( ), ( )... ( ) i i ih  v  v  v  over all paths of length h contained (as sub graphs) in G . In this paper , some bounds for higher Randić index and a method for computing the higher R...