Unicyclic graphs with the fourth extremal Wiener indices

YANG Yu-Jun; CAO Yu-Liang; Wang Guang-Fu

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Unicyclic graphs with the fourth extremal Wiener indices

YANG Yu-Jun 1 *,CAO Yu-Liang 1,Wang Guang-Fu 2

1.School of Mathematics and Information Science, Yantai University,Yantai, Shandong, 264005

2.School of Science, East China Jiaotong University, Nanchang, Jiangxi, 330013

*Correspondence author

#Submitted by

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Funding: NSFC （No.11671347, 11261019）

Opened online:29 March 2017

Accepted by: none

Citation: YANG Yu-Jun,CAO Yu-Liang,Wang Guang-Fu.Unicyclic graphs with the fourth extremal Wiener indices[OL]. [29 March 2017] http://en.paper.edu.cn/en_releasepaper/content/4722647

Unicyclic graphs with the fourth extremal Wiener indices are characterized. It is shown that among all unicyclic graphs with $ngeq 8$ vertices,$C_5(S_{n-4})$ and $C_2^{u_1,u_2}(S_3,S_{n-4})$ have the fourth minimum Wiener indices, whereas $C^{u_1,u_2}_3(P_{3},P_{n-4})$ has the fourth maximum Wiener index.

Keywords:Unicyclic graph; Wiener index; Path; Star

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