Wiener index and Harary index on Hamilton-connected graphs with large minimum degree

Abstract In this paper, we give some sufficient conditions for connected graphs with given minimum degree to be Hamilton-connected and traceable from every vertex in terms of Wiener index and Harary index. We also prove sufficient conditions on Harary index of G ¯ for G to be Hamilton-connected and traceable from every vertex with given minimum degree.

[1]  I. Gutman,et al.  Wiener Index of Hexagonal Systems , 2002 .

[2]  H. Wiener Structural determination of paraffin boiling points. , 1947, Journal of the American Chemical Society.

[3]  Bolian Liu,et al.  A Survey on Recent Results of Variable Wiener Index , 2013 .

[4]  Hongbo Hua,et al.  On Harary Index and Traceable Graphs , 2013 .

[5]  Ovidiu Ivanciuc,et al.  Design of topological indices. Part 4. Reciprocal distance matrix, related local vertex invariants and topological indices , 1993 .

[6]  Bo Zhou,et al.  On Harary index , 2008 .

[7]  Ruifang Liu,et al.  Wiener index on traceable and hamiltonian graphs , 2016 .

[8]  Hongbo Hua,et al.  Wiener index, Harary index and Hamiltonicity of graphs , 2016, 1609.00114.

[9]  Nenad Trinajstić,et al.  Harary Index - Twelve Years Later* , 2002 .

[10]  Xiaomin Zhu,et al.  Wiener index, Harary index and graph properties , 2017, Discret. Appl. Math..

[11]  Kexiang Xu,et al.  The Harary Index of a Graph , 2015 .

[12]  Bo Zhou,et al.  Bounds on Harary index , 2009 .

[13]  N. Trinajstic,et al.  On the Harary index for the characterization of chemical graphs , 1993 .

[14]  Lihui Yang WIENER INDEX AND TRACEABLE GRAPHS , 2012, Bulletin of the Australian Mathematical Society.

[15]  D. Vukicevic,et al.  Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges , 2009 .

[16]  I. Gutman,et al.  Wiener Index of Trees: Theory and Applications , 2001 .

[17]  Ligong Wang,et al.  Wiener-type invariants on graph properties , 2018 .