Harary指数与图的哈密尔顿-连通性
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摘要
如果图G中任意两个顶点都被一条哈密尔顿路相连,则称G是哈密尔顿-连通的。为了得到更好的边界条件,主要利用图及其补图的Harary指数,得到具有最小度条件的连通图是哈密尔顿-连通的两个充分条件,改进了已有的相关结论。
A graph G is said to be Hamilton-connected if every two vertices of its are connected by Hamilton path. To get better boundary conditions, let G be a connected graph with given minimum degree, in terms of Harary index of graph and its complement graph, the paper gives two sufficient conditions for it to be Hamilton-connected which improved relevant conclusions.
A graph G is said to be Hamilton-connected if every two vertices of its are connected by Hamilton path. To get better boundary conditions, let G be a connected graph with given minimum degree, in terms of Harary index of graph and its complement graph, the paper gives two sufficient conditions for it to be Hamilton-connected which improved relevant conclusions.
引文
[1]余桂东.图的哈密尔顿性与连通性的谱刻画[M].合肥:安徽大学出版社,2015.
[2]Plav?i?D,Nikoli?S,Trinajsti?N,et al.On the Harary index for the characterization of chemical graphs[J].Journal of Mathematical Chemistry,1993,12(1):235-250.
[3]Ivanciuc O,Balaban T S,Balaban A T.Reciprocal distance matrix,related local vertex invariants and topological indices[J].Journal of Mathematical Chemistry,1993,12(1):309-318.
[4]Chen M-Z,Zhang X-D.The number of edges,spectral radius and Hamilton-connectedness of graphs[J].Journal of Combinational Optimization,2018,35(2):1-24.
[2]Plav?i?D,Nikoli?S,Trinajsti?N,et al.On the Harary index for the characterization of chemical graphs[J].Journal of Mathematical Chemistry,1993,12(1):235-250.
[3]Ivanciuc O,Balaban T S,Balaban A T.Reciprocal distance matrix,related local vertex invariants and topological indices[J].Journal of Mathematical Chemistry,1993,12(1):309-318.
[4]Chen M-Z,Zhang X-D.The number of edges,spectral radius and Hamilton-connectedness of graphs[J].Journal of Combinational Optimization,2018,35(2):1-24.