A note on nearly Platonic graphs with connectivity one

被引：1
|
作者：
Froncek, Dalibor [1 ]
Khorsandi, Mahdi Reza [2 ]
Musawi, Seyed Reza [2 ]
Qiu, Jiangyi [3 ]
机构：
[1] Univ Minnesota, Dept Math & Stat, Duluth, MN 55812 USA
[2] Shahrood Univ Technol, Fac Math Sci, POB 36199-95161, Shahrood, Iran
[3] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01003 USA
来源：
ELECTRONIC JOURNAL OF GRAPH THEORY AND APPLICATIONS | 2021年 / 9卷 / 01期
关键词：
planar graph; regular graph; Platonic graph;
D O I：
10.5614/ejgta.2021.9.1.17
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A k-regular planar graph G is nearly Platonic when all faces but one are of the same degree while the remaining face is of a different degree. We show that no such graphs with connectivity one can exist. This complements a recent result by Keith, Froncek, and Kreher on non-existence of 2-connected nearly Platonic graphs.
引用
收藏
页码：195 / 205
页数：11
相关论文
共 50 条
  • [21] A Note on Cyclic Connectivity and Matching Properties of Regular Graphs
    Michael D. Plummer
    Tao Wang
    Qinglin Yu
    [J]. Graphs and Combinatorics, 2014, 30 : 1003 - 1011
  • [22] A note on the cyclical edge-connectivity of fullerene graphs
    Qi, Zhongbin
    Zhang, Heping
    [J]. JOURNAL OF MATHEMATICAL CHEMISTRY, 2008, 43 (01) : 134 - 140
  • [23] A note on the eccentric connectivity index of graphs of given diameter
    du Toit, Lindie
    Mukwembi, Simon
    Vetrik, Tomas
    [J]. UTILITAS MATHEMATICA, 2020, 115 : 267 - 274
  • [24] A Note on Cyclic Connectivity and Matching Properties of Regular Graphs
    Plummer, Michael D.
    Wang, Tao
    Yu, Qinglin
    [J]. GRAPHS AND COMBINATORICS, 2014, 30 (04) : 1003 - 1011
  • [25] A NOTE ON EDGE-CONNECTIVITY OF THE CARTESIAN PRODUCT OF GRAPHS
    Fitina, Lakoa
    Lenard, C. T.
    Mills, T. M.
    [J]. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2011, 84 (01) : 171 - 176
  • [26] NOTE ON PLATONIC ANAMNESIS
    WELLMAN, RR
    [J]. EDUCATIONAL THEORY, 1966, 16 (02) : 169 - 175
  • [27] Cheeger constants of Platonic graphs
    Lanphier, D
    Rosenhouse, J
    [J]. DISCRETE MATHEMATICS, 2004, 277 (1-3) : 101 - 113
  • [28] A note on the restricted arc connectivity of oriented graphs of girth four
    Gonzalez-Moreno, D.
    Hernandez Ortiz, R.
    [J]. AUSTRALASIAN JOURNAL OF COMBINATORICS, 2018, 70 : 340 - 348
  • [29] Disentangling Brain Graphs: A Note on the Conflation of Network and Connectivity Analyses
    Simpson, Sean L.
    Laurienti, Paul J.
    [J]. BRAIN CONNECTIVITY, 2016, 6 (02) : 95 - 98
  • [30] Irregular coloring of Join of two graphs and Platonic graphs
    Shyama, S.
    Iyer, Radha R.
    [J]. 2022 2nd International Conference on Computer Science, Engineering and Applications, ICCSEA 2022, 2022,
12345