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October, 2022 On Almost Self-centered Graphs and Almost Peripheral Graphs
Yanan Hu, Xingzhi Zhan
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Taiwanese J. Math. 26(5): 887-901 (October, 2022). DOI: 10.11650/tjm/220401

Abstract

An almost self-centered graph is a connected graph of order $n$ with exactly $n-2$ central vertices, and an almost peripheral graph is a connected graph of order $n$ with exactly $n-1$ peripheral vertices. We determine (1) the maximum girth of an almost self-centered graph of order $n$; (2) the maximum independence number of an almost self-centered graph of order $n$ and radius $r$; (3) the minimum order of a $k$-regular almost self-centered graph; (4) the maximum size of an almost peripheral graph of order $n$; (5) possible maximum degrees of an almost peripheral graph of order $n$ and (6) the maximum number of vertices of maximum degree in an almost peripheral graph of order $n$ with maximum degree $n-4$ which is the second largest possible. Whenever the extremal graphs have a neat form, we also describe them.

Funding Statement

This research was supported by the NSFC grant 11671148 and Science and Technology Commission of Shanghai Municipality (STCSM) grant 18dz2271000.

Citation

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Yanan Hu. Xingzhi Zhan. "On Almost Self-centered Graphs and Almost Peripheral Graphs." Taiwanese J. Math. 26 (5) 887 - 901, October, 2022. https://doi.org/10.11650/tjm/220401

Information

Received: 12 August 2021; Revised: 27 February 2022; Accepted: 10 April 2022; Published: October, 2022
First available in Project Euclid: 14 April 2022

Digital Object Identifier: 10.11650/tjm/220401

Subjects:
Primary: 05C07 , 05C35 , 05C69

Keywords: almost peripheral graph , almost self-centered graph , Girth , independence number

Rights: Copyright © 2022 The Mathematical Society of the Republic of China

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Vol.26 • No. 5 • October, 2022
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