journal-of-discrete-mathematical-sciences-and-cryptography

Journal of Discrete Mathematical Sciences and Cryptography

2169-0065 0972-0529

Taru Publications

10.47974/JDMSC-1824

Pseudo-resolvent energy of weighted graphs

Shukur

Ali A.

Department of Mathematics, Faculty of Computer Science and Mathematics, University of Kufa, An-Najaf, Iraq Faculty of Mechanics and Mathematics, Belarusian State University, Minsk, Belarus Cangul

Ismail Naci

Department of Mathematics, Bursa Uludag University, Bursa, 16059, Turkey

27 6 1831 1837

16 09 2024

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.

Graph energy Resolvent energy of graph Pseudospectrum Non-normal matrix

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