The kth power of a graph G, denoted by Gk , is a graph with the same vertex set as G such that two vertices are adjacent in Gk if and only if their distance is at most k in G. The Wiener index is a distance-based topological index defined as the sum of distances between all pairs of vertices in a graph. In this note, we give the bounds on the Wiener index of the graph Gk . The Nordhaus–Gaddum-t...

The Wiener index W (G) of a connected graph G is defined to be the sum

general formulas are obtained for the vertex padmakar-ivan index (piv) of tetrathiafulvalene(ttf) dendrimer, whereby ttf units we are employed as branching centers. the piv index isa wiener-szeged-like index developed very recently. this topological index is defined as thesummation of all sums of nu(e) and nv(e), over all edges of connected graph g.

the padmakar-ivan (pi) index is a wiener-szeged-like topological index which reflectscertain structural features of organic molecules. the pi index of a graph g is the sum of alledges uv of g of the number of edges which are not equidistant from the vertices u and v. inthis paper we obtain the second and third extremals of catacondensed hexagonal systems withrespect to the pi index.

In the drug design process, one wants to construct chemical compounds with certain properties. In order to establish the mathematical basis for the connections between molecular structures and physicochemical properties of chemical compounds, some so-called structure-descriptors or ”topological indices” have been put forward. Among them, the Wiener index is one of the most important. A long sta...

The unitary Cayley graph Xn has vertex set Zn = {0, 1,…, n-1} and vertices u and v are adjacent, if gcd(uv, n) = 1. In [A. Ilić, The energy of unitary Cayley graphs, Linear Algebra Appl. 431 (2009) 1881–1889], the energy of unitary Cayley graphs is computed. In this paper the Wiener and hyperWiener index of Xn is computed.

The Wiener index of a graph G is equal to the sum of distances between all pairs of vertices of G, It is known that the Wiener index of a molecular graph correlates with certain physical and chemical properties of a molecule. In the mathematical literature, many good algorithms can be found to eompute the distances m a graph, and these can easily be adapted for the caleulation of the Wiener ind...

The Wiener index of a graph G, denoted W(G), is the sum distances between all non-ordered pairs vertices in G.É. Czabarka, et al. conjectured that for simple quadrangulation G on n vertices, n?4, W(G)?112n3+76n?2,n?0(mod2), 112n3+1112n?1,n?1(mod2).In this paper, we confirm conjecture.