Spectral radius and the $2$-power of Hamilton cycles

Xinru Yan; Xiaocong He; Lihua Feng; Weijun Liu

Spectral radius and the $2$-power of Hamilton cycles

Combinatorics 2022-01-14 v1

Authors: Xinru Yan , Xiaocong He , Lihua Feng , Weijun Liu

Abstract

Let $G$ be a graph of order $n$ and spectral radius be the largest eigenvalue of its adjacency matrix, denoted by $\mu(G)$ . In this paper, we determine the unique graph with maximum spectral radius among all graphs of order $n$ without containing the $2$ -power of a Hamilton cycle.

Keywords

spectral radius hamilton cycle graph power adjacency matrix extremal graph

Cite

@article{arxiv.2201.04889,
  title  = {Spectral radius and the $2$-power of Hamilton cycles},
  author = {Xinru Yan and Xiaocong He and Lihua Feng and Weijun Liu},
  journal= {arXiv preprint arXiv:2201.04889},
  year   = {2022}
}

Comments

17 pages, 10 figures

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