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On a generalization of the spectral Mantel’s theorem

Author

Listed:
  • Chunmeng Liu

    (Harbin Engineering University)

  • Changjiang Bu

    (Harbin Engineering University)

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.

Suggested Citation

  • Chunmeng Liu & Changjiang Bu, 2023. "On a generalization of the spectral Mantel’s theorem," Journal of Combinatorial Optimization, Springer, vol. 46(2), pages 1-10, September.
    • Handle: RePEc:spr:jcomop:v:46:y:2023:i:2:d:10.1007_s10878-023-01081-y
    DOI: 10.1007/s10878-023-01081-y
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