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.
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