hansen et‎. ‎al.‎, ‎using the autographix software ‎package‎, ‎conjectured that the szeged index $sz(g)$ and the‎ ‎wiener index $w(g)$ of a connected bipartite graph $g$ with $n geq ‎4$ vertices and $m geq n$ edges‎, ‎obeys the relation‎ ‎$sz(g)-w(g) geq 4n-8$‎. ‎moreover‎, ‎this bound would be the best possible‎. ‎this paper offers a proof to this conjecture‎.

The Wiener polarity indexWP (G) of a graph G is the number of unordered pairs of vertices {u, v} of G such that the distance of u and v is equal to 3. In this paper, we obtain the relation between Wiener polarity index and Zegreb indices, and the relation between Wiener polarity index and Wiener index (resp. hyper-Wiener index). Moreover, we determine the second smallest Wiener polarity index t...

One of the most widely known topological index is the Wiener index. The Wiener Index Conjecture states that all positive integer numbers except a finite set are the Wiener indices of some trees. We explore the Wiener indices of the binary trees. We present efficient algorithms for generating the Wiener indices of the binary trees. Based on experiments we strengthen the conjecture for the class ...

reliability wiener number is a modification of the original wiener number in which probabilities are assigned to edges yielding a natural model in which there are some (or all) bonds in the molecule that are not static. various probabilities naturally allow modelling different types of chemical bonds because chemical bonds are of different types and it is well-known that under certain condition...

 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...