Open Journal of Discrete Applied Mathematics
Vol. 6 (2023), Issue 3, pp. 30 – 34
ISSN: 2617-9687 (Online) 2617-9679 (Print)
DOI: 10.30538/psrp-odam2023.0091
The bounds for topological invariants of a weighted graph using traces
Emre Sevgi\(^{1,*}\), Gül Özkan Kizilirmak\(^{2}\), Serife Büyükköse
\(^{1}\)Department of Mathematics, Faculty of Science, Gazi University, Ankara, Turkey.; emresevgi@gazi.edu.tr; gulozkangazi.edu.tr; sbuyukkose@gazi.edu.tr
Copyright © 2023 Emre Sevgi, Gül Özkan Kizilirmak and Serife Büyükköse. 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: September 15, 2023 – Accepted: November 7, 2023 – Published: December 26, 2023
Abstract
In this paper, we obtain the bounds for the Laplacian eigenvalues of a weighted graph using traces. Then, we find the bounds for the Kirchhoff and Laplacian Estrada indices of a weighted graph. Finally, we define the Laplacian energy of a weighted graph and get the upper bound for this energy.
Keywords:
Laplacian energy; Kirchhoff index; Laplacian Estrada index; Weighted graph.