let r be a commutative ring and (r) be its zerodivisor graph. in this article, we studywiener index and energy of γ(zn ) where n = pq or n = p2q and p, q are primes. a matlabcode for our calculations is also presented.

Old and new results for characterizing volume forms in functional integration. 1 The Wiener measure Defining volume forms on infinite dimensional spaces is a key problem in the theory of functional integration. The first volume form used in functional integration has been the Wiener measure. From the several equivalent definitions of the Wiener measure, we choose one [1] which can easily be ext...

It is well known that the vertices of any graph can be put in a linear preorder so that for random walk on the graph vertices appearing earlier in the preorder are “easier to reach but more difficult to get out of”. We exhibit further such preorders corresponding to various functions related to random walk and study their relationships. These preorders coincide when the graph is a tree, but not...

In this paper, we give solutions for the two conjectures on the inverse problem of the Wiener index of peptoids proposed by Goldman et al. We give the first conjecture a positive proof and the second conjecture a negative answer.

Among the variety of molecular-graph-based structure-descriptors, aimed at measuring the extent of branching of the skeleton of organic molecules, there are the Wiener index W and the spectral radius λ1 i. e., the greatest eigenvalue of the molecular graph. Although, these indices are used for decades, they have never been compared. Our computational studies show that within series of the isome...

Polynomial interpolation can be used to obtain closed formulas for topological indices of infinite series of molecular graphs. The method is discussed and its advantages and limitations are pointed out. This is illustrated on fullerenes C12k+4 and four topological indices: the Wiener index, the edge Wiener index, the eccentric connectivity index, and the reverse Wiener index. The results for th...

The Wiener index of a graph is the sum of all pairwise distances of vertices of the graph. Fischermann et al [5] characterized the trees which minimize the Wiener index among all trees with the maximum degree at most ∆. They also determined the trees which maximize the Wiener index, but in a much more restricted family of trees which have two distinct vertex degrees only. In this note, we fully...