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Open Journal of Discrete Applied Mathematics (ODAM)

ISSN: 2617-9687 (Online) 2617-9679 (Print)
  • DOI: https://www.doi.org/10.30538/psrp-odam2023.0091
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  • Research article

The bounds for topological invariants of a weighted graph using traces

Author(s): Emre Sevgi1, Gül Özkan Kizilirmak, Serife Büyükköse
1Department of Mathematics, Faculty of Science, Gazi University, Ankara, Turkey.
Copyright © Emre Sevgi, Gül Özkan Kizilirmak, 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: 15/09/2023
  • Accepted: 07/11/2023
  • Published: 26/12/2023

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.
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