Abstract. Applications of isometric embeddings of benzenoid graphs are surveyed. Their embeddings into hypercubes provide methods for computing the Wiener index and the Szeged index, while embeddings into the Cartesian product of trees lead to fast algorithms. A new method for computing the hyperWiener index of partial cubes in general, and of benzenoid graphs and trees in particular, is also p...

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 ≥ 4 vertices and m ≥ n edges, obeys the relation Sz(G) − W (G) ≥ 4n − 8. Moreover, this bound would be the best possible. This paper offers a proof to this conjecture.

In theoretical chemistry, molecular structure descriptors are used to compute properties of chemical compounds. Among them Wiener, Szeged and detour indices play significant roles in anticipating chemical phenomena. In the present paper, we study these topological indices with respect to their difference number.

let $d$ be a digraph with vertex set $v(d)$. for vertex $vin v(d)$, the degree of $v$,denoted by $d(v)$, is defined as the minimum value if its out-degree and its in-degree.now let $d$ be a digraph with minimum degree $deltage 1$ and edge-connectivity$lambda$. if $alpha$ is real number, then the zeroth-order general randic index is definedby $sum_{xin v(d)}(d(x))^{alpha}$. a digraph is maximall...

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.

the topological indices, defined as the sum of contributions of all pairs of vertices (among which are the wiener, harary, hyper–wiener indices, degree distance, and many others), are expressed in terms of contributions of edges and pairs of edges.

Zoltan Alexin Department of Informatics University of Szeged [email protected]—szeged.hu Tibor Gyinnithy Research Group on Artifical Intelligence at University of Szeged [email protected]—szeged.hu Csaba Hatvani Department of Informatics University of Szeged [email protected]—szeged.hu LaszlO Tihanyi MorphoLogic Budapest [email protected] Janos Csirik Department of Informatics University of Szeged csiri...