On the Szeged and Wiener complexities in graphs

Modjtaba Ghorbani and Zahra Vaziri

Applied Mathematics and Computation, 2024, vol. 470, issue C

Abstract: When characterizing networks structurally, the discriminating ability of a topological index is crucial. This relates to investigate its discrimination power (also called uniqueness or degeneracy) that indicates how meaningful the given measure can distinguish nonisomorphic networks. Assume G is a connected graph. The Szeged complexity (or briefly Sz-complexity) of a graph G is the number of different portions in the Szeged index formula. Also, the Wiener complexity (or briefly W-complexity) can be defined similarly. In the current work, we study graphs with small Sz-complexity. We characterize trees with Sz-complexity two and bicyclic graphs with Sz-complexity one. In this way, first we introduce some graphs with Sz-complexity one. For instance, we investigate Θ-graph and two categories of k-cyclic graphs. Besides, we classify bicyclic graphs with Sz-complexity equal to the number of edge-orbits. Finally, we determine W-complexity of these graphs.

Keywords: Szeged complexity; Wiener complexity; Θ-graph; Bicyclic graphs (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:470:y:2024:i:c:s0096300324000043

DOI: 10.1016/j.amc.2024.128532

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