scholarly journals Sufficient conditions for Hamilton-connected graphs in terms of (signless Laplacian) spectral radius

2020 ◽  
Vol 594 ◽  
pp. 205-225
Author(s):  
Qiannan Zhou ◽  
Ligong Wang ◽  
Yong Lu
Keyword(s):  
Spectral Radius ◽  
Sufficient Conditions ◽  
Laplacian Spectral Radius ◽  
Connected Graphs ◽  
Signless Laplacian Spectral Radius ◽  
Signless Laplacian ◽  
Hamilton Connected

On the distance signless Laplacian spectral radius of graphs and digraphs

2017 ◽  
Vol 32 ◽  
pp. 438-446 ◽  
Author(s):  
Dan Li ◽  
Guoping Wang ◽  
Jixiang Meng
Keyword(s):  
Spectral Radius ◽  
Connected Graph ◽  
Minimum Degree ◽  
Extremal Graph ◽  
Minimal Distance ◽  
Vertex Connectivity ◽  
Laplacian Spectral Radius ◽  
Connected Graphs ◽  
Signless Laplacian Spectral Radius ◽  
Signless Laplacian

Let \eta(G) denote the distance signless Laplacian spectral radius of a connected graph G. In this paper,bounds for the distance signless Laplacian spectral radius of connected graphs are given, and the extremal graph with the minimal distance signless Laplacian spectral radius among the graphs with given vertex connectivity and minimum degree is determined. Furthermore, the digraph that minimizes the distance signless Laplacian spectral radius with given vertex connectivity is characterized.

scholarly journals Spectral Sufficient Conditions on Pancyclic Graphs

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Guidong Yu ◽  
Tao Yu ◽  
Xiangwei Xia ◽  
Huan Xu
Keyword(s):  
Spectral Radius ◽  
Spectral Theory ◽  
Sufficient Conditions ◽  
Laplacian Spectral Radius ◽  
Signless Laplacian Spectral Radius ◽  
Signless Laplacian ◽  
Np Complete ◽  
Pancyclic Graphs ◽  
Theory Of Graphs ◽  
Spectrum Of Graphs

A pancyclic graph of order n is a graph with cycles of all possible lengths from 3 to n . In fact, it is NP-complete that deciding whether a graph is pancyclic. Because the spectrum of graphs is convenient to be calculated, in this study, we try to use the spectral theory of graphs to study this problem and give some sufficient conditions for a graph to be pancyclic in terms of the spectral radius and the signless Laplacian spectral radius of the graph.

scholarly journals Signless Laplacian Spectral Conditions for Hamiltonicity of Graphs

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Guidong Yu ◽  
Miaolin Ye ◽  
Gaixiang Cai ◽  
Jinde Cao
Keyword(s):  
Spectral Radius ◽  
Laplacian Spectral Radius ◽  
Signless Laplacian Spectral Radius ◽  
Signless Laplacian ◽  
Hamilton Connected

We establish some signless Laplacian spectral radius conditions for a graph to be Hamiltonian or traceable or Hamilton-connected.

scholarly journals Spectral Conditions for a Graph to be Hamilton-Connected

2013 ◽  
Vol 336-338 ◽  
pp. 2329-2334 ◽  
Author(s):  
Gui Dong Yu ◽  
Yi Zheng Fan
Keyword(s):  
Spectral Radius ◽  
Adjacency Matrix ◽  
Laplacian Spectral Radius ◽  
Hamiltonian Paths ◽  
Signless Laplacian Spectral Radius ◽  
Signless Laplacian ◽  
Hamilton Connected

Some spectral conditions for a graph to be Hamilton-connected in terms of the spectral radius of the adjacency matrix or signless Laplacian of the graph or its complement are established, and then the condition on the signless Laplacian spectral radius of a graph for the existence of Hamiltonian paths or cycles is given.

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