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

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.

A survey on spectral conditions for some extremal graph problems

“…The following version of the signless Laplacian spectral radius is a special case of Theorem 3.19, which will be introduced in next subsection. Theorem 3.12 (Cheng et al [39]). Let δ ≥ 1 and n ≥ δ 4 + 9δ 3 + 24δ 2 + 23δ + 15.…”

“…Here, the symbol B n,k,δ \ E ′ stands for the subgraph of B n,k,δ by deleting all edges from the edge set E ′ . Recently, Cheng, Feng, Li and Liu [39] proved the following extension on the sufficient conditions of the existence of a Hamilton path.…”