The Moore Bound for Irregular Graphs

被引：0
|
作者：
Noga Alon
Shlomo Hoory
Nathan Linial
机构：
[1] Mathematics and Computer Science,
[2] Sackler Faculty of Exact Sciences,undefined
[3] Tel Aviv University,undefined
[4] Tel Aviv,undefined
[5] Israel. e-mail: noga@math.tau.ac.il,undefined
[6] Institute of Computer Science,undefined
[7] Hebrew University,undefined
[8] Jerusalem 91904,undefined
[9] Israel e-mail: shlomoh@cs.huji.ac.il,undefined
[10] Institute of Computer Science,undefined
[11] Hebrew University,undefined
[12] Jerusalem 91904,undefined
[13] Israel e-mail: nati@cs.huji.ac.il,undefined
来源：
Graphs and Combinatorics | 2002年 / 18卷
关键词：
Open Problem; Affirmative Answer; Irregular Graph;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
 What is the largest number of edges in a graph of order n and girth g? For d-regular graphs, essentially the best known answer is provided by the Moore bound. This result is extended here to cover irregular graphs as well, yielding an affirmative answer to an old open problem ([4] p. 163, problem 10).
引用
收藏
页码：53 / 57
页数：4
相关论文
共 50 条
  • [1] The Moore bound for irregular graphs
    Alon, N
    Hoory, S
    Linial, N
    [J]. GRAPHS AND COMBINATORICS, 2002, 18 (01) : 53 - 57
  • [2] A revised Moore bound for mixed graphs
    Buset, Dominique
    El Amiri, Mourad
    Erskine, Grahame
    Miller, Mirka
    Perez-Roses, Hebert
    [J]. DISCRETE MATHEMATICS, 2016, 339 (08) : 2066 - 2069
  • [3] A SPECTRAL MOORE BOUND FOR BIPARTITE SEMIREGULAR GRAPHS
    Lato, Sabrina
    [J]. SIAM JOURNAL ON DISCRETE MATHEMATICS, 2023, 37 (01) : 315 - 331
  • [4] Approaching the Moore bound for diameter two by Cayley graphs
    Siagiova, Jana
    Siran, Jozef
    [J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 2012, 102 (02) : 470 - 473
  • [5] Graphs of order two less than the Moore bound
    Miller, Mirka
    Simanjuntak, Rinovia
    [J]. DISCRETE MATHEMATICS, 2008, 308 (13) : 2810 - 2821
  • [6] Approaching the mixed Moore bound for diameter two by Cayley graphs
    Siagiova, Jana
    [J]. AUSTRALASIAN JOURNAL OF COMBINATORICS, 2015, 61 : 73 - 81
  • [7] Asymptotically approaching the Moore bound for diameter three by Cayley graphs
    Bachraty, Martin
    Siagiova, Jana
    Siran, Jozef
    [J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 2019, 134 : 203 - 217
  • [8] On Total Regularity of Mixed Graphs with Order Close to the Moore Bound
    James Tuite
    Grahame Erskine
    [J]. Graphs and Combinatorics, 2019, 35 : 1253 - 1272
  • [9] On Total Regularity of Mixed Graphs with Order Close to the Moore Bound
    Tuite, James
    Erskine, Grahame
    [J]. GRAPHS AND COMBINATORICS, 2019, 35 (06) : 1253 - 1272
  • [10] THERE IS NO IRREGULAR MOORE GRAPH
    SINGLETON, R
    [J]. AMERICAN MATHEMATICAL MONTHLY, 1968, 75 (01): : 42 - +
12345