A note on the graph’s resolvent and the multifilar structure |
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Authors: | Vladimir Ejov |
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Institution: | a School of Mathematics of Statistics, University of South Australia, Australia b Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, United States |
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Abstract: | We consider the recently discovered V. Ejov, J.A. Filar, S.K. Lucas, P. Zograf, Clustering of spectra and fractals of regular graphs, J. Math. Anal. Appl. 333 (2007) 236-246] threadlike structure of the plot representing d-regular graphs in the mean-variance coordinates of exponential sums of the graph spectra. In this note we demonstrate that this self-similar phenomenon is more ubiquitous by exhibiting it with the help of a different generating function, namely the mean and the variance of the resolvent of the adjacency matrix of the graph. We also discuss the location of non-Hamiltonian graphs within this geometric structure. |
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Keywords: | 05C45 05C75 11M36 |
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