The sum of distances between all the pairs of vertices in a connected graph is known as the {it Wiener index} of the graph. In this paper, we obtain the Wiener index of edge complements of stars, complete subgraphs and cycles in $K_n$.

a lot of research and various techniques have been devoted for finding the topologicaldescriptor wiener index, but most of them deal with only particular cases. there exist threeregular plane tessellations, composed of the same kind of regular polygons namely triangular,square, and hexagonal. using edge congestion-sum problem, we devise a method to computethe wiener index and demonstrate this m...

Abstract. A subgraph H of a graph G is gated if for every x ∈ V (G) there exists a vertex u in H such that dG(x, v) = dG(x, u) + dG(u, v) for any v ∈ V (H). The gated amalgam of graphs G1 and G2 is obtained from G1 and G2 by identifying their isomorphic gated subgraphs H1 and H2. Two theorems on the Wiener index of gated amalgams are proved. Several known results on the Wiener index of (chemica...

Introduced in 1947, the Wiener index W (T ) = ∑ {u,v}⊆V (T ) d(u, v) is one of the most thoroughly studied chemical indices. The extremal structures (in particular, trees with various constraints) that maximize or minimize the Wiener index have been extensively investigated. The Harary index H(T ) = ∑ {u,v}⊆V (T ) 1 d(u,v) , introduced in 1993, can be considered as the “reciprocal analogue” of ...

Let G be a simple graph with vertex set and edge set . The function which assigns to each pair of vertices in , the length of minimal path from to , is called the distance function between two vertices. The distance function between and edge and a vertex is where for and. , . The Wiener index of a graph is denoted by and is defined by .In general this kind of index is called a topological index...

Let d(G, k) be the number of pairs of vertices of a graph G that are at distance k, λ a real number, and Wλ(G) = ∑ k≥1 d(G, k)kλ. Wλ(G) is called the Wiener-type invariant of G associated to real number λ. In this paper, the Wiener-type invariants of some graph operations are computed. As immediate consequences, the formulae for reciprocal Wiener index, Harary index, hyperWiener index and Tratc...

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 $g$ ...

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.