Open Journal of Discrete Applied Mathematics
Vol. 6 (2023), Issue 2, pp. 1 – 6
ISSN: 2617-9687 (Online) 2617-9679 (Print)
DOI: 10.30538/psrp-odam2023.0083
On the product of Sombor and modified Sombor indices
Ivan Gutman\(^{1,*}\), Izudin Redžepović\(^{2}\) and Boris Furtula\(^{1}\)
\(^{1}\) Faculty of Science, University of Kragujevac, 34000 Kragujevac, Serbia; gutman@kg.ac.rs; (I. G.) furtula@uni.kg.ac.rs (B. F.)
\(^{2}\) State University of Novi Pazar, 36300 Novi Pazar, Serbia; iredzepovic@np.ac.rs (I.R.)
Copyright © 2023 Ivan Gutman, Redžepović and Boris Furtula . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: May 22, 2023 – Accepted: August 04, 2023 – Published: October 23, 2023
Abstract
The Sombor index (\(SO\)) and the modified Sombor index (\(^mSO\)) are two closely related vertex-degree-based graph invariants. Both were introduced in the 2020s, and have already found a variety of chemical, physicochemical, and network-theoretical applications. In this paper, we examine the product \(SO \cdot {^mSO}\) and determine its main properties. It is found that the structure-dependence of this product is fully different from that of either \(SO\) or \(^mSO\). Lower and upper bounds for \(SO \cdot {^mSO}\) are established and the extremal graphs are characterized. For connected graphs, the minimum value of the product \(SO \cdot {^mSO}\) is the square of the number of edges. In the case of trees, the maximum value pertains to a special type of eclipsed sun graph, trees with a single branching point.
Keywords:
Sombor index; modified Sombor index; topological index; degree (of vertex).