the wiener index $w(g)$ of a connected graph $g$‎ ‎is defined as $w(g)=sum_{u,vin v(g)}d_g(u,v)$‎ ‎where $d_g(u,v)$ is the distance between the vertices $u$ and $v$ of‎ ‎$g$‎. ‎for $ssubseteq v(g)$‎, ‎the {it steiner distance/} $d(s)$ of‎ ‎the vertices of $s$ is the minimum size of a connected subgraph of‎ ‎$g$ whose vertex set is $s$‎. ‎the {it $k$-th steiner wiener index/}‎ ‎$sw_k(g)$ of $g$ ...

let $g$ be a molecular graph with vertex set $v(g)$, $d_g(u, v)$ the topological distance between vertices $u$ and $v$ in $g$. the hosoya polynomial $h(g, x)$ of $g$ is a polynomial $sumlimits_{{u, v}subseteq v(g)}x^{d_g(u, v)}$ in variable $x$. in this paper, we obtain an explicit analytical expression for the expected value of the hosoya polynomial of a random benzenoid chain with $n$ hexagon...

Let $G$ be a molecular graph with vertex set $V(G)$, $d_G(u, v)$ the topological distance between vertices $u$ and $v$ in $G$. The Hosoya polynomial $H(G, x)$ of $G$ is a polynomial $sumlimits_{{u, v}subseteq V(G)}x^{d_G(u, v)}$ in variable $x$. In this paper, we obtain an explicit analytical expression for the expected value of the Hosoya polynomial of a random benzenoid chain with $n$ hexagon...

The Wiener index, denoted byW (G), of a connected graph G is the sum of all pairwise distances of vertices of the graph, that is, W (G) = 1 2 ∑ u,v∈V (G) d(u, v). In this paper, we obtain the Wiener index of the tensor product of a path and a cycle.

The Wiener index of a graph G is defined to be 2 , ( ) ( , ), u V G d u ∈ ∑ X X where d(u, X) is the distance between the vertices u and X in G. In this paper, we obtain an explicit expression for the Wiener index of an odd graph.

The Wiener index, defined as the total sum of distances in a graph, is one of the most popular graph-theoretical indices. Its average value has been determined for several classes of trees, giving an asymptotics of the form Kn5/2 for some K. In this note, it is shown how the method can be extended to trees with restricted degrees. Particular emphasis is placed on chemical trees – trees with max...

Abstract The n-th order Wiener index of a molecular graph G was put forward by Estrada et al. [New J. Chem. 22 (1998) 819] as ( ) 1 ( , ) n n x W H G x where ( , ) H G x is the Hosoya polynomial. Recently Brückler et al. [Chem. Phys. Lett. 503 (2011) 336] considered a related graph invariant, ( ) 1 1 (1/ !) ( ( , )) / n n n n x W n d x H G x d x . For n=1, both W and W reduce to the ordinary W...