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Answers to Gould's question concerning the existence of chorded cycles
Leyou Xu, Bo Zhou
Answers are offered to the Gould's question to find spectral sufficient conditions for a graph to have a chorded cycle via signless Laplacian spectral radius. The conditions are ti…
Distribution of signless Laplacian eigenvalues and graph invariants
Leyou Xu, Bo Zhou
For a simple graph on vertices, any of its signless Laplacian eigenvalues is in the interval . In this paper, we give relationships between the number of signless La…
Link residual closeness of graphs with fixed parameters
Leyou Xu, Chengli Li, Bo Zhou
Link residual closeness is a newly proposed measure for network vulnerability. In this model, vertices are perfectly reliable and the links fail independently of each other. It mea…
Toughness and existence of -factors
Leyou Xu, Bo Zhou
A graph is -tough if the deletion of any set of, say, vertices from the graph leaves a graph with at most components. In 1973, Chvátal suggested the problem of…
The Alon-Tarsi number of -minor-free graphs
Leyou Xu, Bo Zhou
The well known Wagner's theorem states that a graph is a planar graph if and only if it is -minor-free and -minor-free. Denote by the Alon-Tarsi number of a g…
Laplacain eigenvalue distribution and diameter of graphs
Leyou Xu, Bo Zhou
Let be a connected graph on vertices with diameter . It is known that if , there are at most Laplacian eigenvalues in the interval . In…
The generalized -connectivity of bubble-sort graphs
Leyou Xu, Bo Zhou
For with , let denote the maximum number of internally disjoint trees connecting in . For , the generalized -connectivi…
Hamiltonicity of -tough -free graphs
Leyou Xu, Chengli Li, Bo Zhou
Given a graph , a graph is -free if does not contain as an induced subgraph. For a positive real number , a non-complete graph is said to be -tough if f…
Normalized Laplacian eigenvalues of hypergraphs
Leyou Xu, Bo Zhou
In this paper, we give tight bounds for the normalized Laplacian eigenvalues of hypergraphs that are not necessarily uniform, and provide an edge version interlacing theorem, a Che…
Proof of a conjecture on distribution of Laplacian eigenvalues and diameter, and beyond
Leyou Xu, Bo Zhou
Ahanjideh, Akbari, Fakharan and Trevisan proposed a conjecture in [Linear Algebra Appl. 632 (2022) 1--14] on the distribution of the Laplacian eigenvalues of graphs: for any connec…