Extended Schatten norms of random graphs and Nikiforov conjecture

Authors : Ivan LAZAREVİC

Pages : 737-742

Doi:10.15672/hujms.914884

View : 24 | Download : 11

Publication Date : 2022-06-01

Article Type : Research Paper

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