Girth 5 graphs from relative difference sets

被引：15
|
作者：
Jorgensen, LK [1 ]
机构：
[1] Univ Aalborg, Dept Math Sci, DK-9220 Aalborg, Denmark
来源：
DISCRETE MATHEMATICS | 2005年 / 293卷 / 1-3期
关键词：
cage; girth; Cayley graph; relative difference set;
D O I：
10.1016/j.disc.2004.08.029
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the problem of construction of graphs with given degree k and girth 5 and as few vertices as possible. We give a construction of a family of girth 5 graphs based on relative difference sets. This family contains the smallest known graph of degree 8 and girth 5 which was constructed by Royle, four of the known cages including the Hoffman-Singleton graph, some graphs constructed by Exoo and some new smallest known graphs. (c) 2005 Elsevier B.V. All rights reserved.
引用
收藏
页码：177 / 184
页数：8
相关论文
共 50 条
  • [1] Relative difference sets fixed by inversion and Cayley graphs
    Chen, YQ
    Li, CH
    JOURNAL OF COMBINATORIAL THEORY SERIES A, 2005, 111 (01) : 165 - 173
  • [2] Relative difference sets in Alt(5)
    Hiramine, Y
    JOURNAL OF COMBINATORIAL THEORY SERIES A, 2005, 110 (02) : 179 - 191
  • [3] Stopping sets and the girth of tanner graphs
    Orlitsky, A
    Urbanke, R
    Viswanathan, K
    Zhang, J
    ISIT: 2002 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, PROCEEDINGS, 2002, : 2 - 2
  • [4] Girth 5 Graphs from Elliptic Semiplanes
    Funk, M.
    NOTE DI MATEMATICA, 2009, 29 : 91 - 113
  • [5] Relative Difference Sets, Graphs and Inequivalence of Functions Between Groups
    Horadam, K. J.
    JOURNAL OF COMBINATORIAL DESIGNS, 2010, 18 (04) : 260 - 273
  • [6] INDEPENDENT SETS IN REGULAR GRAPHS OF HIGH GIRTH
    MCKAY, BD
    ARS COMBINATORIA, 1987, 23A : 179 - 185
  • [7] Locating-Dominating Sets and Identifying Codes in Graphs of Girth at least 5
    Balbuena, Camino
    Foucaud, Florent
    Hansberg, Adriana
    ELECTRONIC JOURNAL OF COMBINATORICS, 2015, 22 (02):
  • [8] Independent dominating sets in graphs of girth five
    Harutyunyan, Ararat
    Horn, Paul
    Verstraete, Jacques
    COMBINATORICS PROBABILITY & COMPUTING, 2021, 30 (03): : 344 - 359
  • [9] Sparse sets in the complements of graphs with given girth
    Kostochka, AV
    Woodall, DR
    DISCRETE MATHEMATICS, 2001, 233 (1-3) : 163 - 174
  • [10] COMPUTING INDEPENDENT SETS IN GRAPHS WITH LARGE GIRTH
    MURPHY, OJ
    DISCRETE APPLIED MATHEMATICS, 1992, 35 (02) : 167 - 170
12345