- Hacettepe Journal of Mathematics and Statistics
- Vol: 51 Issue: 3
- Extended Schatten norms of random graphs and Nikiforov conjecture
Extended Schatten norms of random graphs and Nikiforov conjecture
Authors : Ivan Lazarevic
Pages : 737-742
Doi:10.15672/hujms.914884
View : 10 | Download : 5
Publication Date : 2022-06-01
Article Type : Research
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