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Sharp Bounds for Wiener Index of Maximal Outerplanar Graphs

School of Mathematics and System Sciences, Xinjiang University, Urumqi Xinjiang 830017, China
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Abstract

A graph is outerplanar if it has a crossing-free embedding in the plane such that all vertices are on the boundary of its outer face. An outerplanar graph is maximal outerplanar if no edge can be added without losing outerplanarity. The Wiener index of a graph G is the sum of distances between all pairs of vertices of G. We show that for a maximal outerplanar graph G on n vertices, W(K1∨Pn−1) ≤W(G)≤W( Pn2), where K1∨Pn−1 is the graph obtained from joining a vertex to each vertex of Pn−1 and Pn2 is the square of Pn.

Keywords

maximal outerplanar graphWiener indexextremal graphssquare graphs
CLC number: O157.5 Document code: A Article ID: 2096-7675(2023)05-0560-05

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Journal of Xinjiang University(Natural Science Edition in Chinese and English)
Volume 40 Issue 5,
September 2023
Pages 560-564
DOI: 10.13568/j.cnki.651094.651316.2023.01.04.0001

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Cite this article:
SUN X, AN X. Sharp Bounds for Wiener Index of Maximal Outerplanar Graphs. Journal of Xinjiang University(Natural Science Edition in Chinese and English), 2023, 40(5): 560-564. https://doi.org/10.13568/j.cnki.651094.651316.2023.01.04.0001

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Received: 04 January 2023
Published: 01 September 2023
© 2023 Journal of Xinjiang University (Natural Science Edition in Chinese and English)