# Wiener index, Harary index and Hamiltonicity of graphs

@article{Hua2016WienerIH, title={Wiener index, Harary index and Hamiltonicity of graphs}, author={Hongbo Hua and Bo Ning}, journal={arXiv: Combinatorics}, year={2016} }

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…

#### 14 Citations

Wiener Index, Hyper-wiener Index, Harary Index and Hamiltonicity of graphs

- Mathematics
- 2018

In this paper, we discuss the Hamiltonicity of graphs in terms of Wiener index, hyper-Wiener index and Harary index of their quasi-complement or complement. Firstly, we give some sufficient…

Wiener Index, Hyper-Wiener Index, Harary Index and Hamiltonicity Properties of graphs

- MathematicsApplied Mathematics-A Journal of Chinese Universities
- 2019

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.…

Sufficient Conditions for Hamiltonicity of Graphs with Respect to Wiener Index, Hyper-Wiener Index, and Harary Index

- Chemistry
- 2019

In this paper, with respect to the Wiener index, hyper-Wiener index, and Harary index, it gives some sufficient conditions for some graphs to be traceable, Hamiltonian, Hamilton-connected, or…

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

- Computer Science, MathematicsDiscret. Appl. Math.
- 2018

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 are given.

Wiener index and Harary index on pancyclic graphs.

- Mathematics
- 2019

Wiener index and Harary index are two classic and well-known topological indices for the characterization of molecular graphs. Recently, Yu et al. \cite{YYSX} established some sufficient conditions…

Metric properties of generalized Sierpiński graphs over stars

- Mathematics, Computer ScienceDiscret. Appl. Math.
- 2019

The Wiener index, the Wiener complexity, and the metric dimension of their antipode family S K 1 , n t are determined and along the way some other properties of the family are obtained such as the number of vertex and edge orbits of the automorphism group.

Distance and Eccentric sequences to bound the Wiener index, Hosoya polynomial and the average eccentricity in the strong products of graphs

- Computer Science, MathematicsDiscret. Appl. Math.
- 2019

It is shown that for fixed H, and G chosen from among all connected graphs of given order n , it is maximised if G is a path of the same order.

On the peripheral Wiener index of graphs

- Computer Science, MathematicsDiscret. Appl. Math.
- 2019

Two sharp lower and upper bounds on the peripheral Wiener index for graphs without cut vertices are given and two sharp upper bounds are established in terms of other distance-based graph invariants.

Maximum Detour-Harary Index for Some Graph Classes

- Mathematics, Computer ScienceSymmetry
- 2018

This paper has obtained the maximum Detour–Harary index about unicyclic graphs, bicyclic graph, and cacti, respectively.

On graphs whose Wiener complexity equals their order and on Wiener index of asymmetric graphs

- Mathematics, Computer ScienceAppl. Math. Comput.
- 2018

It is proved that almost no graphs are transmission irregular, and the Wiener index of T is bounded by (n3−13n+48)/6 with equality if and only if T=T1,2,n−4.

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