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.
The reciprocal degree resistance distance index of a connected graph G is defined as RDRG=∑u,v⊆VGdGu+dGv/rGu,v, where rGu,v is the resistance distance between vertices u and v in G. Let Un denote the set of unicyclic graphs with n vertices. We study the graph with maximum reciprocal degree resistance distance index among all graphs in Un and characterize the corresponding extremal graph.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.