The stress of a vertex is node centrality index, which has been introduced by Shimbel (1953). in graph the number geodesics (shortest paths) passing through it. In this paper, we introduce new topological index for graphs called square root sum using stresses vertices. Further, establish some inequalities, prove results and compute stress-sum standard graphs.

Topological indices are the mathematical tools that correlate the chemical structure with various physical properties, chemical reactivity or biological activity numerically. A topological index is a function having a set of graphs as its domain and a set of real numbers as its range. In QSAR/QSPR study, a prediction about the bioactivity of chemical compounds is made on the basis of physico-ch...

we derived explicit formulae for the eccentric connectivity index and wiener index of2-dimensional square-octagonal tuc4c8(r) lattices with open and closed ends. newcompression factors for both indices are also computed in the limit n-->∞.

In this note, we derive the lower bound on the sum for Wiener index of bipartite graph and its bipartite complement, as well as the lower and upper bounds on this sum for the Randić index and Zagreb indices. We also discuss the quality of these bounds.

Let G be a simple connected graph and t be a given real number. The zero-order general Randić index αt(G) of G is defined as ∑ v∈V (G) d(v) t , where d(v) denotes the degree of v. In this paper, for any t , we characterize the graphs with the greatest and the smallest αt within two subclasses of connected unicyclic graphs on n vertices, namely, unicyclic graphs with k pendant vertices and unicy...

The Randić index R(G) of a graph G is defined as the sum of 1 √dudv over all edges uv of G, where du and dv are the degrees of vertices u and v, respectively. Let D(G) be the diameter of Gwhen G is connected. Aouchiche et al. (2007) [1] conjectured that among all connected graphs G on n vertices the path Pn achieves the minimum values for both R(G)/D(G) and R(G) − D(G). We prove this conjecture...