Qualitative, statistical and extreme properties of spectral indices of signable pseudo-invertible graphs

2024/03/07 by Soña Pavlíková, Pavlikova, Sona, Daniel Ševčovič +1
Mathematics · #Graph theory and applications #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2403.04902

Abstract

In this paper, we investigate the Moore-Penrose inversion of a simple connected graph. We analyze qualitative, statistical, and extreme properties of spectral indices of signable pseudo-invertible graphs. We introduce and analyze a wide class of signable pseudo-invertible simple connected graphs. It is a generalization of the classical concept of positively integrally invertible graphs due to Godsil. We present several constructions of signable pseudo-invertible graphs. We also discuss statistical properties of various spectral indices of the class of signable pseudo-invertible graphs.

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