 The work is supported by Training and plan projects of college students' innovation and pioneering in Guangdong Province(No.1056412059). Abstract Wiener index proposed by Harold Wiener in 1947 is a very important topological index which is widely applied in chemical research. Gutman et al. extended the Wiener index to variable Wiener index. M. H. Liu et al. obtained the maximum variable Wiene...

wiener index is a topological index based on distance between every pair of vertices in agraph g. it was introduced in 1947 by one of the pioneer of this area e.g, harold wiener. inthe present paper, by using a new method introduced by klavžar we compute the wiener andszeged indices of some nanostar dendrimers.

let g be a molecular graph. the wiener index of g is defined as the summation of alldistances between vertices of g. in this paper, an exact formula for the wiener index of a newtype of nanostar dendrimer is given.

in this paper, the degree distance and the gutman index of the corona product of two graphs are determined. using the results obtained, the exact degree distance and gutman index of certain classes of graphs are computed.

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.

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.

By the Von Neumann regular graph of R, we mean the graph that its vertices are all elements of R such that there is an edge between vertices x,y if and only if x+y is a von Neumann regular element of R, denoted by G_Vnr (R). For a commutative ring R with unity, x in R is called Von Neumann regular if there exists x in R such that a=a2 x. We denote the set of Von Neumann regular elements by V nr...