Publication Date
1-1-2026
Document Type
Article
Publication Title
Match
Volume
95
Issue
2
DOI
10.46793/match.95-2.05425
First Page
457
Last Page
466
Abstract
The energy ε(G) of a graph G is the sum of the absolute values of all the eigenvalues of its adjacency matrix. Gutman (2001) pointed out a problem to characterize the graph G and the edge e of G such that ε(G − e) ⩽ ε(G). Tang et al. (2023) gave a sufficient condition for ε(G − e) ⩽ ε(G), where e is not necessarily a cut-edge set or a cut edge. We deduce here a stronger conclusion than the results obtained by Tang et al. (2023). Our findings cover some known conclusions, such as the results obtained by Gutman and Pavlović (1999) and Tang et al. (2023). In addition, based on the new results we obtained in this article, we can directly conclude that adding edges to a complete k-partite graph leads to a graph with a higher energy than the energy of the original graph.
Funding Number
21ZR1423500
Funding Sponsor
Natural Science Foundation of Shanghai Municipality
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Department
Mathematics and Statistics
Recommended Citation
Huan Lei Shi, Wen Huan Wang, and Wasin So. "The Energy Change of Graphs under Some Edges Deletions" Match (2026): 457-466. https://doi.org/10.46793/match.95-2.05425
