Extended Schatten norms of random graphs and Nikiforov conjecture

Year 2022, Volume: 51 Issue: 3, 737 - 742, 01.06.2022

Ivan Lazarevic

https://doi.org/10.15672/hujms.914884

Abstract

In this paper we give mean of $p$-th degree of singular values and upper bound of geometric mean for almost all graphs. We prove three theorems about a conjecture of V. Nikiforov for Schatten $p$-norm of graphs when $p>2$. We prove that the conjecture is true when $p$ is an even integer or when graph is a tree or a strongly regular graph with certain parameters. The strongly regular graphs with these parameters are graphs with maximal energy.

Keywords

singular values of graph, Schatten norms, random graph, energy of graph

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