arXiv subjects

Gui-Dong Yu

Publications and source records attributed to Gui-Dong Yu.

3 recordsLinked to original sources

arXiv2018

Maximum reciprocal degree resistance distance index of unicyclic graphs

The reciprocal degree resistance distance index of a connected graph $G$ is defined as $RDR(G)=\sum\limits_{\{u,v\}\subseteq V(G)}\frac {d_G(u)+d_G(v)}{r_G(u,v)}$, where $r_G(u,v)$ is the resistance distance between vertices $u$ and $v$ in $G$. Let $\mathscr {U}_n$ denote the set of unicyclic graphs with $n$ vertices. We study the graph with maximum reciprocal degree resistance distance index among all graphs in $\mathscr {U}_n$, and characterize the corresponding extremal graph.

math.CO↗

arXiv2012

Spectral Condition for a Graph to be Hamiltonian with respect to Normalized Laplacian

Let G be a graph and let Δ,δbe the maximum and minimum degrees of G respectively, where Δ/δ<c<\sqrt{2} and c is a constant. In this paper we establish a sufficient spectral condition for the graph G to be Hamiltonian, that is, the nontrivial eigenvalues of the normalized Laplacian of G are sufficiently close to 1.

math.CO↗

arXiv2012

Spectral conditions for a graph to be Hamilton-connected

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.

math.CO↗