The vertex version of PI index is a molecular structure descriptor which is similar to vertex version of Szeged index. In this paper, we compute the vertex-PI index of TUC4C8(S), TUC4C8(R) and HAC5C7[r, p].

Let e be an edge of a G connecting the vertices u and v. Define two sets N1 (e | G) and N2(e |G) as N1(e | G)= {xV(G) d(x,u) d(x,v)} and N2(e | G)= {xV(G) d(x,v) d(x,u) }.The number of elements of N1(e | G) and N2(e | G) are denoted by n1(e | G) and n2(e | G) , respectively. The Szeged index of the graph G is defined as Sz(G) ( ) ( ) 1 2 n e G n e G e E    . In this paper we compute th...

We resolve two conjectures of Hri\v{n}\'{a}kov\'{a}, Knor and \v{S}krekovski (2019) concerning the relationship between variable Wiener index Szeged for a connected, non-complete graph, one which would imply other. The strong conjecture is that any such graph there critical exponent in $(0,1]$, below larger above larger. weak always exceeding $1$. They proved bipartite graphs, trees. In this no...

ABSTRACT Let ‎G=(V,E) ‎be a‎ ‎simple ‎connected ‎graph ‎with ‎vertex ‎set ‎V‎‎‎ ‎and ‎edge ‎set ‎‎‎E. ‎The Szeged index ‎of ‎‎G is defined by ‎ where ‎ respectively ‎ ‎ is the number of vertices of ‎G ‎closer to ‎u‎ (‎‎respectively v)‎ ‎‎than ‎‎‎v (‎‎respectively u‎).‎ ‎‎If ‎‎‎‎S ‎is a‎ ‎set ‎of ‎size‎ ‎ ‎ ‎let ‎‎V ‎be ‎the ‎set ‎of ‎all ‎subsets ‎of ‎‎S ‎of ‎size ‎3. ‎Then ‎we ‎define ‎t...

In this paper the Wiener and hyper Wiener index of two kinds of dendrimer graphs are determined. Using the Wiener index formula, the Szeged, Schultz, PI and Gutman indices of these graphs are also determined.

Abstract Topological indices of nanotubes are numerical descriptors that are derived from graph of chemical compounds. Such indices based on the distances in graph are widely used for establishing relationships between the structure of nanotubes and their physico-chemical properties. The Szeged index is obtained as a bond additive quantity where bond contributions are given as the product of th...

e=uv∈E(nu(e)+n0(e)/2)(nv(e)+n0(e)/2), where nu(e) and nv(e) are, respectively, the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex v than to vertex u, and n0(e) is the number of vertices equidistant to u and v. Hansen used the AutoGraphiX and made the following conjecture about the revised Szeged index for a connected bicy...