Spectral conditions for a graph to be Hamilton-connected

Abstract

In this paper we establish some spectral conditions for a graph to be Hamilton-connected in terms of the spectral radius of the adjacency matrix or the signless Laplacian of the graph or its complement. For the existence of Hamiltonian paths or cycles in a graph, we also give a sufficient condition by the signless Laplacian spectral radius.

Cited by in corpus (10)

• Spectral analogues of Erdős' and Moon-Moser's theorems on Hamilton cycles
• Spectral Condition for a Graph to be Hamiltonian with respect to Normalized Laplacian
• A tight $Q$-index condition for a graph to be $k$-path-coverable involving minimum degree
• Sufficient spectral conditions for graphs being $k$-edge-Hamiltonian or $k$-Hamiltonian
• Some Sufficient Conditions on Pancyclic Graphs
• Unified spectral hamiltonian results of balanced bipartite graphs and complementary graphs
• Signless Laplacian spectral conditions for Hamilton-connected graphs with large minimum degree
• Sufficient spectral conditions on Hamiltonian and traceable graphs
• The signless Laplacian spectral radius of graphs with forbidding linear forests
• A note on eigenvalues and Hamiltoinan properties of $k$-connected graphs