whereas there is an exact linear relation between the wiener indices of kenograms and plerograms of isomeric alkanes, the respective terminal wiener indices exhibit a completely different behavior: correlation between terminal wiener indices of kenograms and plerograms is absent, but other regularities can be envisaged. in this article, we analyze the basic properties of terminal wiener indices...

the wiener polarity index wp(g) of a molecular graph g of order n is the number ofunordered pairs of vertices u, v of g such that the distance d(u,v) between u and v is 3. in anearlier paper, some extremal properties of this graph invariant in the class of catacondensedhexagonal systems and fullerene graphs were investigated. in this paper, some new bounds forthis graph invariant are presented....

Whereas there is an exact linear relation between the Wiener indices of kenograms and plerograms of isomeric alkanes, the respective terminal Wiener indices exhibit a completely different behavior: Correlation between terminal Wiener indices of kenograms and plerograms is absent, but other regularities can be envisaged. In this article, we analyze the basic properties of terminal Wiener indices...

Abstract. In this paper Reverse Wiener index, Reverse Detour Wiener index, Reverse Circular Wiener index Reverse Harary index, Reverse Detour Harary index, Reverse Circular Harary index, Reverse Reciprocal Wiener index, Reverse Detour Reciprocal Wiener index, Reverse Circular Reciprocal Wiener index, Reverse Hyper Wiener index, Reverse, Detour Hyper Wiener index, Reverse Circular Hyper Wiener i...

the wiener index is a graph invariant that has found extensive application in chemistry. inaddition to that a generating function, which was called the wiener polynomial, who’sderivate is a q-analog of the wiener index was defined. in an article, sagan, yeh and zhang in[the wiener polynomial of a graph, int. j. quantun chem., 60 (1996), 959969] attainedwhat graph operations do to the wiener po...

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.

The Wiener index of a connected graph G, denoted by W(G) , is defined as ∑ ( , ) , ∈ ( ) .Similarly, hyper-Wiener index of a connected graph G,denoted by WW(G), is defined as ( ) + ∑ ( , ) , ∈ ( ) .In this paper, we present the explicit formulae for the Wiener, hyper-Wiener and reverse Wiener indices of some graph operations. Using the results obtained here, the exact formulae for Wiener, hyper...

the unitary cayley graph xn has vertex set zn = {0, 1,…, n-1} and vertices u and v areadjacent, if gcd(uv, n) = 1. in [a. ilić, the energy of unitary cayley graphs, linear algebraappl. 431 (2009) 1881–1889], the energy of unitary cayley graphs is computed. in this paperthe wiener and hyperwiener index of xn is computed.

motivated by the terminal wiener index‎, ‎we define the ashwini index $mathcal{a}$ of trees as‎ begin{eqnarray*}‎ % ‎nonumber to remove numbering (before each equation)‎ ‎mathcal{a}(t) &=& sumlimits_{1leq i‎&+& deg_{_{t}}(n(v_{j}))],‎ ‎end{eqnarray*}‎ ‎where $d_{t}(v_{i}‎, ‎v_{j})$ is the distance between the vertices $v_{i}‎, ‎v_{j} in v(t)$‎, ‎is equal to the length of the shortest path start...

this note introduces a new general conjecture correlating the dimensionality dt of an infinitelattice with n nodes to the asymptotic value of its wiener index w(n). in the limit of large nthe general asymptotic behavior w(n)≈ns is proposed, where the exponent s and dt are relatedby the conjectured formula s=2+1/dt allowing a new definition of dimensionality dw=(s-2)-1.being related to the topol...