STRUCTURAL PROPERTIES OF GRAPHS OF DIAMETER 2 AND DEFECT 2

被引:0
|
作者
Minh Hoang Nguyen [1 ,2 ]
Miller, Mirka [1 ,3 ,4 ]
机构
[1] Univ Newcastle, Fac Engn & Built Environm, Sch Elect Engn & Comp Sci, Callaghan, NSW 2308, Australia
[2] Ericsson Australia Pty Ltd, Tower B 112-118 Talavera Rd, N Ryde, NSW 2113, Australia
[3] Univ West Bohemia, Dept Math, Plzen, Czech Republic
[4] Kings Coll London, Dept Comp Sci, London WC2R 2LS, England
基金
澳大利亚研究理事会;
关键词
Diameter; repeat set; repeat subgraph;
D O I
暂无
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Using eigenvalue analysis, it was shown by Erdos et al. that with the exception of C-4, there are no graphs of diameter 2, maximum degree d and d(2) vertices. In this paper, we prove a number of structural properties of regular graphs of diameter 2, maximum degree d and order d(2) - 1.
引用
收藏
页码:29 / 43
页数:15
相关论文
共 50 条
  • [31] ON MOORE GRAPHS WITH DIAMETER-2 AND DIAMETER-3
    HOFFMAN, AJ
    SINGLETON, RR
    IBM JOURNAL OF RESEARCH AND DEVELOPMENT, 1960, 4 (05) : 497 - 504
  • [32] On the existence of graphs of diameter two and defect two
    Conde, J.
    Gimbert, J.
    DISCRETE MATHEMATICS, 2009, 309 (10) : 3166 - 3172
  • [33] 2-Diameter of de Bruijn graphs
    Li, Q
    Sotteau, D
    Xu, JM
    NETWORKS, 1996, 28 (01) : 7 - 14
  • [34] PRIMITIVE DIAMETER 2-CRITICAL GRAPHS
    Radosavljevic, Jovan
    Stanic, Zoran
    Zivkovic, Miodrag
    PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD, 2024, 115 (129): : 21 - 32
  • [35] Diameter Constraints in 2-distance Graphs
    Al-Saadi, Oleksiy
    Natal, Joseph
    arXiv,
  • [36] MINIMUM EDGE CUTS IN DIAMETER 2 GRAPHS
    Bickle, Allan
    Schwenk, Allen
    DISCUSSIONES MATHEMATICAE GRAPH THEORY, 2019, 39 (02) : 605 - 608
  • [37] MAXIMUM DEGREE IN GRAPHS OF DIAMETER-2
    ERDOS, P
    FAJTLOWICZ, S
    HOFFMAN, AJ
    NETWORKS, 1980, 10 (01) : 87 - 90
  • [38] The domination game played on diameter 2 graphs
    Bujtas, Csilla
    Irsic, Vesna
    Klavzar, Sandi
    Xu, Kexiang
    AEQUATIONES MATHEMATICAE, 2022, 96 (01) : 187 - 199
  • [39] The Thresholds for Diameter 2 in Random Cayley Graphs
    Christofides, Demetres
    Markstrom, Klas
    RANDOM STRUCTURES & ALGORITHMS, 2014, 45 (02) : 218 - 235
  • [40] Sufficient conditions for λ′-optimality in graphs of diameter 2
    Hellwig, A
    Volkmann, L
    DISCRETE MATHEMATICS, 2004, 283 (1-3) : 113 - 120