A characterization of graphs with at most four boundary vertices

被引：0

作者：

Chiem, Nick ^{[1
]}

Dudarov, William ^{[2
]}

Lee, Chris ^{[2
]}

Lee, Sean ^{[2
]}

Liu, Kevin ^{[2
]}

机构：

[1] Univ Calif Riverside, Dept Math, Riverside, CA 92521 USA

[2] Univ Washington, Dept Math, Seattle, WA 98125 USA

来源：

JOURNAL OF COMBINATORICS | 2024年 / 15卷 / 03期

关键词：

STRONG METRIC DIMENSION; SETS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Steinerberger defined a notion of boundary for a graph and established a corresponding isoperimetric inquality. Hence, "large" graphs have more boundary vertices. In this paper, we first characterize graphs with three boundary vertices in terms of two infinite families of graphs. We then completely characterize graphs with four boundary vertices in terms of eight families of graphs, five of which are infinite. This parallels earlier work by Hasegawa and Saito as well as Mu<spacing diaeresis>ller, Po<acute accent>r, and Sereni on another notion of boundary defined by Chartrand, Erwin, Johns, and Zhang. AMS 2000 SUBJECT CLASSIFICATIONS: Primary 05C12, 05C75. KEYWORDS AND PHRASES: Graph, boundary, isoperimetric inequality, metric space, extremal.

引用

页码：361 / 382

页数：22

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