Wiener指数,hyper-Wiener指数与图的哈密尔顿-连通性
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摘要
如果图中任意两顶点都被一条哈密尔顿路相连,则称它是哈密尔顿-连通的。本文主要利用图及其补图的Wiener指数、hyper-Wiener指数,给出了具有最小度条件的连通图是哈密尔顿-连通的充分条件。
A graph is said to be Hamilton-connected if every two vertices of its are connected by Hamilton path. In this paper,let G be a connected graph with given minimum degree,in terms of Wiener index,hyper-Wiener index of graph and its complement graph,we give some sufficient conditions for it to be Hamilton-connected.
A graph is said to be Hamilton-connected if every two vertices of its are connected by Hamilton path. In this paper,let G be a connected graph with given minimum degree,in terms of Wiener index,hyper-Wiener index of graph and its complement graph,we give some sufficient conditions for it to be Hamilton-connected.
引文
[1] Wiener H. Structural determination of paraffin boiling points[J]. Journal of the American Chemical Society,1947,69(1):17
[2] Randi?M. Novel molecular descriptor for structure—property studies☆[J]. Chemical Physics Letters,1993,211(4-5):478-483
[3] Klein D J,Lukovits I,Gutman I. On the Definition of the Hyper-Wiener Index for Cycle-Containing Structures[J]. Journal of Chemical Information&Modeling,1995,35(1):50-52
[4] Hua H, Ning B. Wiener index, Harary index and Hamiltonicity of graphs[J]. Match Communications in Mathematical&in Computer Chemistry, 2016, 78(1):153-162
[5] G.-X Cai,M.-L. Ye,Y. Gui,R. Li. Hyper-Wiener index and Hamiltonicity of graphs[J]. Ars Combinatoria,accepted
[6]Liu R, Xue D U, Jia H. WIENER INDEX ON TRACEABLE AND HAMILTONIAN?GRAPHS[J].Bulletin of the Australian Mathematical Society,2016,94(3):362-372
[7]Liu R,Du X,Jia H. Some Observations on Harary Index and Traceable Graphs[J]. Match Communications in Mathematical&in Computer Chemistry,2017,77(1):195-208
[8]Chen M Z,Zhang X D. The number of edges,spectral radius and Hamilton-connectedness of graphs[J].Journal of Combinatorial Optimization,2018(2):1-24
[2] Randi?M. Novel molecular descriptor for structure—property studies☆[J]. Chemical Physics Letters,1993,211(4-5):478-483
[3] Klein D J,Lukovits I,Gutman I. On the Definition of the Hyper-Wiener Index for Cycle-Containing Structures[J]. Journal of Chemical Information&Modeling,1995,35(1):50-52
[4] Hua H, Ning B. Wiener index, Harary index and Hamiltonicity of graphs[J]. Match Communications in Mathematical&in Computer Chemistry, 2016, 78(1):153-162
[5] G.-X Cai,M.-L. Ye,Y. Gui,R. Li. Hyper-Wiener index and Hamiltonicity of graphs[J]. Ars Combinatoria,accepted
[6]Liu R, Xue D U, Jia H. WIENER INDEX ON TRACEABLE AND HAMILTONIAN?GRAPHS[J].Bulletin of the Australian Mathematical Society,2016,94(3):362-372
[7]Liu R,Du X,Jia H. Some Observations on Harary Index and Traceable Graphs[J]. Match Communications in Mathematical&in Computer Chemistry,2017,77(1):195-208
[8]Chen M Z,Zhang X D. The number of edges,spectral radius and Hamilton-connectedness of graphs[J].Journal of Combinatorial Optimization,2018(2):1-24