Year: 2019
Type: article
Abstract: The weighted (edge‐)Szeged index and the weighted (vertex‐)PI index are modifications of the (edge‐)Szeged index and the (vertex‐)PI index, respectively, because they take into account also the vertex degrees. As the main result of this article, we prove that if G is a connected graph, then all these indices can be computed in terms of the corresponding indices of weighted quotient graphs with respect to a partition of the edge set that is coarser than the Θ * ‐partition. If G is a benzenoid system or a phenylene, then it is possible to choose a partition of the edge set in such a way that the quotient graphs are trees. As a consequence, it is shown that for a benzenoid system, the mentioned indices can be computed in sublinear time with respect to the number of vertices. Moreover, closed formulas for linear phenylenes are also deduced.
DOI: 10.1002/qua.26006
Author: Niko Tratnik
Institution: University of Maribor
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2954514639