In this paper, in terms of Wiener index, hyper-Wiener index and Harary index, we first give some sufficient conditions for a nearly balance bipartite graph with given minimum degree to be traceable. Secondly, we estab...In this paper, in terms of Wiener index, hyper-Wiener index and Harary index, we first give some sufficient conditions for a nearly balance bipartite graph with given minimum degree to be traceable. Secondly, we establish some conditions for a k-connected graph to be Hamilton-connected and traceable for every vertex, respectively.展开更多
Let G be a 3-connected graph with n vertices, is an independent set of G} , MC(G)=min is an independent set in G}.In this paper, the main results are as follows.TheoremⅠ. If then G is Hamilton-connected.TheoremⅡ. If...Let G be a 3-connected graph with n vertices, is an independent set of G} , MC(G)=min is an independent set in G}.In this paper, the main results are as follows.TheoremⅠ. If then G is Hamilton-connected.TheoremⅡ. If, then G is Hamilton-connected.Theorems I and IIare the best possible, and are incomparable in the sense that neither theorem implies the other.展开更多
基金Supported by the Natural Science Foundation of China under Grant no(11871077)the NSF of Anhui Province of China under Grant no(1808085MA04)the Natural Science Foundation of Department of Education of Anhui Province of China under Grant no(KJ2017A362)
文摘In this paper, in terms of Wiener index, hyper-Wiener index and Harary index, we first give some sufficient conditions for a nearly balance bipartite graph with given minimum degree to be traceable. Secondly, we establish some conditions for a k-connected graph to be Hamilton-connected and traceable for every vertex, respectively.
文摘Let G be a 3-connected graph with n vertices, is an independent set of G} , MC(G)=min is an independent set in G}.In this paper, the main results are as follows.TheoremⅠ. If then G is Hamilton-connected.TheoremⅡ. If, then G is Hamilton-connected.Theorems I and IIare the best possible, and are incomparable in the sense that neither theorem implies the other.
