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WIENER INDEX ON TRACEABLE AND HAMILTONIAN GRAPHS

Part of: Graph theory

Published online by Cambridge University Press:  30 August 2016

RUIFANG LIU ,
XUE DU  and
HUICAI JIA
RUIFANG LIU*
Affiliation:
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, China email rfliu@zzu.edu.cn
XUE DU
Affiliation:
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, China email 15225101865@163.com
HUICAI JIA
Affiliation:
College of Science, Henan Institute of Engineering, Zhengzhou, Henan 451191, China email jhc607@163.com
*
✉rfliu@zzu.edu.cn
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Abstract

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We give sufficient conditions for a graph to be traceable and Hamiltonian in terms of the Wiener index and the complement of the graph, which correct and extend the result of Yang [‘Wiener index and traceable graphs’, Bull. Aust. Math. Soc.88 (2013), 380–383]. We also present sufficient conditions for a bipartite graph to be traceable and Hamiltonian in terms of its Wiener index and quasicomplement. Finally, we give sufficient conditions for a graph or a bipartite graph to be traceable and Hamiltonian in terms of its distance spectral radius.

Keywords

complementtraceable graphHamiltonian graphquasicomplementbipartite graphWiener indexdistance spectral radius

MSC classification

Primary: 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 94 , Issue 3 , December 2016 , pp. 362 - 372
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

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