Spectral conditions for the existence of specified paths and cycles in graphs

Mingqing Zhai; Huiqiu Lin; Shicai Gong

Spectral conditions for the existence of specified paths and cycles in graphs

Combinatorics 2013-09-27 v1

Authors: Mingqing Zhai , Huiqiu Lin , Shicai Gong

Abstract

Let $G$ be a graph with $n$ vertices and $\lambda_n(G)$ be the least eigenvalue of its adjacency matrix of $G$ . In this paper, we give sharp bounds on the least eigenvalue of graphs without given pathes or cycles and determine the extremal graphs. This result gives spectral conditions for the existence of specified paths and cycles in graphs.

Keywords

spectral graph theory least eigenvalue adjacency matrix paths and cycles extremal graphs spectral conditions

Cite

@article{arxiv.1309.6700,
  title  = {Spectral conditions for the existence of specified paths and cycles in graphs},
  author = {Mingqing Zhai and Huiqiu Lin and Shicai Gong},
  journal= {arXiv preprint arXiv:1309.6700},
  year   = {2013}
}

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