A tight $Q$-index condition for a graph to be $k$-path-coverable involving minimum degree

Tao Cheng; Lihua Feng; Yongtao Li; Weijun Liu

A tight $Q$-index condition for a graph to be $k$-path-coverable involving minimum degree

Combinatorics 2021-09-16 v1 Spectral Theory

Authors: Tao Cheng , Lihua Feng , Yongtao Li , Weijun Liu

Abstract

A graph $G$ is $k$ -path-coverable if its vertex set $V(G)$ can be covered by $k$ or fewer vertex disjoint paths. In this paper, using the $Q$ -index of a connected graph $G$ , we present a tight sufficient condition for $G$ with fixed minimum degree and large order to be $k$ -path-coverable.

Keywords

graph connectivity graph pebbling graph theory

Cite

@article{arxiv.2109.07347,
  title  = {A tight $Q$-index condition for a graph to be $k$-path-coverable involving minimum degree},
  author = {Tao Cheng and Lihua Feng and Yongtao Li and Weijun Liu},
  journal= {arXiv preprint arXiv:2109.07347},
  year   = {2021}
}

Comments

13 pages. Any comments and suggestions are welcome

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