12 papers
Spectral radius and maximum matching covered graphs with bounded matching number
Xinying Tang, Wenqian Zhang
Let be a graph. The {\em spectral radius} of is the largest eigenvalue of its {\em adjacency matrix}. A {\em matching} of is a set of disjoint edges of . The {\em ma…
A lower bound of toughness of regular graphs: in terms of second largest eigenvalue
Wenqian Zhang
Let be a connected (non-complete) -regular graph with . Let denote the number of components of for any cut of . The toughness of is…
Some lemmas on spectral radius of graphs: including an application
Wenqian Zhang
For a graph , the spectral radius of is the largest eigenvalue of its adjacency matrix. In this paper, we give three lammas on when contains a spanning com…
How to find all extremal graphs using symmetric subgraphs
Wenqian Zhang
Let be a finite family of graphs with , where is the chromatic number of . Set . Let ${\r…
Spectral extrema of graphs forbidding a fan
Wenqian Zhang
For a graph , its spectral radius is the largest eigenvalue of its adjacency matrix. A fan is a graph obtained by connecting a single vertex to all vertices of a path…
Spectral conditions for graphs to contain -factors
Xinying Tang, Wenqian Zhang
Let be a graph. The spectral radius of is the largest eigenvalue of its adjacency matrix. For an integer , a -factor of is a -regular spanning subg…
A spectral condition for Hamilton cycles in tough bipartite graphs
Lianyang Ai, Wenqian Zhang
Let be a graph. The {\em spectral radius} of is the largest eigenvalue of its adjacency matrix. For a non-complete bipartite graph with parts and , the {\em bipa…
Extremal graphs for disjoint union of vertex-critical graphs
Wenqian Zhang
For a graph , let be the set of -free graphs of order with the maximum number of edges. The graph is called vertex-critical, if the deletion of its so…
Spectral skeletons and applications
Wenqian Zhang
For a graph , its spectral radius is the largest eigenvalue of its adjacency matrix. Let be a finite family of graphs with $\min_{F\in \mathcal{F}}χ(F)=r+1\…
A tight upper bound of spectral radius in terms of degree deviation
Wenqian Zhang
Let be a graph with vertices and edges. The spectral radius of is the largest eigenvalue of the adjacency matrix of . As is well known, $ρ(G)\geq\frac{2m}…
Eigenvalues, edge-disjoint perfect matchings and toughness of regular graphs
Wenqian Zhang
Let be a connected -regular graph of order , where . Let be the second largest eigenvalue of . For even , we show that contains $\left\lfloor…
More results on the spectral radius of graphs with no odd wheels
Wenqian Zhang
For a graph , the spectral radius of is the largest eigenvalue of its adjacency matrix. An odd wheel with is a graph obtained from a cycle of…