English

Wiener index, Harary index and Hamiltonicity of graphs

Combinatorics 2017-01-30 v2

Abstract

In this paper, we prove tight sufficient conditions for traceability and Hamiltonicity of connected graphs with given minimum degree, in terms of Wiener index and Harary index. We also prove some result on Hamiltonicity of balanced bipartite graphs in the similar fashion. In two recent papers \cite{LDJ2016,LDJ2017}, Liu et al. corrected some previous work on traceability of connected graphs in terms of Wiener index and Harary index, respectively, such as \cite{HW2013,Y2013}. We generalize these results and give short and unified proofs. All results in this paper are best possible.

Keywords

Cite

@article{arxiv.1609.00114,
  title  = {Wiener index, Harary index and Hamiltonicity of graphs},
  author = {Hongbo Hua and Bo Ning},
  journal= {arXiv preprint arXiv:1609.00114},
  year   = {2017}
}

Comments

11 pages, finial version for publication in MATCH Commun. Math. Comput. Chem