Abstract
For , a
-factor of a graph G is a spanning subgraph F of G such that each component of F is a path with at least k vertices. A graph G is a
-factor covered graph if for each edge e in
, there exists a
-factor containing the edge e. Let
and
be the signless Laplacian matrix and the distance matrix of a graph G, respectively. In this paper, we provide lower bounds for the spectral radius of
in an n-vertex connected graph to guarantee that G has a
-factor or is a
-factor covered graph. Furthermore, we establish upper bounds for the spectral radius of
in an n-vertex connected graph to guarantee that G has a
-factor or is a
-factor covered graph.
Acknowledgements
The authors are greatly indebted to the referee for helpful comments.
Disclosure statement
No potential conflict of interest was reported by the author(s).