Publication: Pseudo-resolvent energy of weighted graphs
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Cangül, İsmail Naci
Authors
Shukur, Ali A.
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Taru Publications
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Abstract
Let G be a finite order graph. Its resolvent matrix and its resolvent energy are respectively given by R xi ( A ( G )) = (A(G) - xi I)-1 -1 and ER ( G ) = Sigma n n i = 1 (n - lambda i)-1. i ) -1 . For some classes of weighted graphs, we know that lambda 1 1 = 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 lambda 1 1 = n.
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Keywords
Graph energy, Resolvent energy of graph, Pseudospectrum, Non-normal matrix, Science & technology, Physical sciences, Mathematics, applied, Mathematics