Edge-Szeged and vertex-PIindices of Some Benzenoid Systems

Some results on vertex-edge Wiener polynomials and indices of graphs

The vertex-edge Wiener polynomials of a simple connected graph are defined based on the distances between vertices and edges of that graph. The first derivative of these polynomials at one are called the vertex-edge Wiener indices. In this paper, we express some basic properties of the first and second vertex-edge Wiener polynomials of simple connected graphs and compare the first and second ve...

Wiener, Szeged and vertex PI indices of regular tessellations

A lot of research and various techniques have been devoted for finding the topological descriptor Wiener index, but most of them deal with only particular cases. There exist three regular plane tessellations, composed of the same kind of regular polygons namely triangular, square, and hexagonal. Using edge congestion-sum problem, we devise a method to compute the Wiener index and demonstrate th...

Labeling of Benzenoid Systems which Reflects the Vertex-Distance Relations

It is shown that the vertices of benzenoid systems admit a labeling which reflects their distance relations. To every vertex of a molecular graph of a benzenoid hydrocarbon a sequence of zeros and ones (a binary number) can be associated, such that the number of positions in which these sequences differ is equal to the graph-theoretic vertex distance. It is shown by an example that such labelin...

The Wiener Index and the Szeged Index of Benzenoid Systems in Linear Time

Distance properties of molecular graphs form an important topic in chemical graph theory.1 To justify this statement just recall the famous Wiener index which is also known as the Wiener number. This index is the first2 but also one of the most important topological indices of chemical graphs. Its research is still very active; see recent reviews3,4 and several new results in a volume5 dedicate...

PI, Szeged and Edge Szeged Polynomials of a Dendrimer Nanostar

Let G be a graph with vertex and edge sets V(G) and E(G), respectively. As usual, the distance between the vertices u and v of a connected graph G is denoted by d(u,v) and it is defined as the number of edges in a minimal path connecting the vertices u and v. Throughout the paper, a graph means undirected connected graph without loops and multiple edges. In chemical graph theory, a molecular gr...

On the Szeged Index of Unbranched Catacondensed Benzenoid Molecules