科研之友
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摘要
For k >= 2, a P >= k-factor of a graph G is a spanning subgraph F of G such that each component of Fis a path with at leastkvertices. AgraphGis a P >= k-factor covered graph if for each edgeein E(G),there exists a P >= k-factor containing the edgee. Let Q(G) and D(G) be the signless Laplacian matrix and the distance matrix of a graph G, respectively. In this paper, we provide lower bounds for the spec-tral radius ofQ(G)in ann-vertex connected graph to guarantee that G has a P >= 2-factor or is a P >= 2-factor covered graph. Further more,we establish upper bounds for the spectral radius of D(G) in ann-vertex connected graph to guarantee that G has aP >= 2-factor or is aP >= 2-factor covered graph
