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Journal of Discrete Mathematical Sciences and Cryptography

(Since 1998)
Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

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Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

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Journal of Discrete Mathematical Sciences and Cryptography
Open Access Research Article

Pseudo-resolvent energy of weighted graphs

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pp. 1831–1837Vol. 27Issue 6September 2024DOI: 10.47974/JDMSC-1824 Crossmark XML
Received:
11 Apr 2023
Published Online:
16 Sep 2024
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-1824
Pages:
1831–1837

Abstract

Let G be a finite order graph. Its resolvent matrix and its resolvent energy are respectively given by Rξ(A(G)) = (A(G) – ξI)–1 and ER(G) = Σni = 1 (n – λi)–1. For some classes of weighted graphs, we know that λ1 = n which means that the formula for ER(G) is not applicable. In this work, the pseudo-resolvent energy for those classes of graphs are obtained where λ1 = n. 

Keywords

Graph energyResolvent energy of graphPseudospectrumNon-normal matrix

Subject Classifications

05C5094C15

References

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