On a generalization of the spectral Mantel’s theorem

Chunmeng Liu () and Changjiang Bu ()
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Chunmeng Liu: Harbin Engineering University
Changjiang Bu: Harbin Engineering University

Journal of Combinatorial Optimization, 2023, vol. 46, issue 2, No 5, 10 pages

Abstract: Abstract Mantel’s theorem is a classical result in extremal graph theory which implies that the maximum number of edges of a triangle-free graph of order n. In 1970, Nosal obtained a spectral version of Mantel’s theorem which gave the maximum spectral radius of a triangle-free graph of order n. In this paper, the clique tensor of a graph G is proposed and the spectral Mantel’s theorem is extended via the clique tensor. Furthermore, a sharp upper bound of the number of cliques in G via the spectral radius of the clique tensor is obtained. These results imply that a result of Erdős (Magyar Tud Akad Mat Kutató Int Közl 7:459–464, 1962) under certain conditions.

Keywords: Mantel’s theorem; Spectral radius; Cliques; Tensor; 05C35; 05C50 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10878-023-01081-y

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