A graph is called k-extendable if each k-matching can be extended to a perfect matching.In this paper,we provide a sufficient condition in terms of the Aa-spectral radius for the k-extendability of a connected graph a...A graph is called k-extendable if each k-matching can be extended to a perfect matching.In this paper,we provide a sufficient condition in terms of the Aa-spectral radius for the k-extendability of a connected graph and characterize the corresponding extremal graphs.In addition,such an A_(α)-spectral condition of a connected balanced bipartite graph is also considered,and the corresponding extremal graphs are determined.展开更多
A connected graph G is said to be k- extendable if it has a set of k independent edges and each set of k independent edges in G can be extended to a perfect matching Qf G. A graph G is k-factor-critical if G - S has a...A connected graph G is said to be k- extendable if it has a set of k independent edges and each set of k independent edges in G can be extended to a perfect matching Qf G. A graph G is k-factor-critical if G - S has a perfect matching for any k-subset S of V（G）. The basic properties of k-extendable and k-factor-critical graphs have been investigated in [11] and [13]. In this paper, we determine thresholds for k-factor-critical graphs and k- extendable bipartite graphs. For non-bipartite k-extendable graphs, we find a probability sequence, which acts the same way like a threshold.展开更多
基金Supported by the National Natural Science Foundation of China(11961041,12261055)the Key Project of Natural Science Foundation of Gansu Province(24JRRA222)。
文摘A graph is called k-extendable if each k-matching can be extended to a perfect matching.In this paper,we provide a sufficient condition in terms of the Aa-spectral radius for the k-extendability of a connected graph and characterize the corresponding extremal graphs.In addition,such an A_(α)-spectral condition of a connected balanced bipartite graph is also considered,and the corresponding extremal graphs are determined.
文摘A connected graph G is said to be k- extendable if it has a set of k independent edges and each set of k independent edges in G can be extended to a perfect matching Qf G. A graph G is k-factor-critical if G - S has a perfect matching for any k-subset S of V（G）. The basic properties of k-extendable and k-factor-critical graphs have been investigated in [11] and [13]. In this paper, we determine thresholds for k-factor-critical graphs and k- extendable bipartite graphs. For non-bipartite k-extendable graphs, we find a probability sequence, which acts the same way like a threshold.
