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) = Σn i = 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.
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