Abstract
The Wiener index is a topological index of a molecular graph, defined as the sum of distances between all pairs of its vertices. Benzenoid graphs include molecular graphs of polycyclic aromatic hydrocarbons. An edge thorny graph G is constructed from a catacondensed benzenoid graph H by attaching new graphs to edges of a perfect matching of H. A formula for the Wiener index of G is derived. The index of the resulting graph does not contain distance characteristics of elements of H and depends on the Wiener index of H and distance properties of the attached graphs.
Highlights
In this paper we deal with finite undirected connected graphs G with vertex set V ( G )
An edge thorny graph is a kind of composite graph
It is obtained by attaching new graphs to the edges of an original benzenoid graph H
Summary
In this paper we deal with finite undirected connected graphs G with vertex set V ( G ). The Wiener index of the thorny graph does not depend on distance properties of vertices of G in some cases. This concept found a variety of chemical applications [23,24,25,26,27,28,29,30,31,32,33]. The specific property of thorny graphs is preserved: the index of the resulting graph does not contain distance characteristics of vertices of H and depends on the Wiener index of H and distance properties of the attached graphs
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