Krein parameters and antipodal tight graphs with diameter 3 and 4

被引：30
|
作者：
Jurisic, A
Koolen, J
机构：
[1] IMFM, Nova Gorica, Slovenia
[2] Nova Gorica Polytech, Nova Gorica, Slovenia
[3] Univ Bielefeld, FSP, D-33501 Bielefeld, Germany
来源：
DISCRETE MATHEMATICS | 2002年 / 244卷 / 1-3期
关键词：
Krein parameters; distance-regular graphs; tight graphs; 1-homogeneous graphs; antipodal graphs; locally strongly-regular; Taylor graphs;
D O I：
10.1016/S0012-365X(01)00082-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We determine which Krein parameters of nonbipartite antipodal distance-regular graphs of diameter 3 and 4 can vanish, and give combinatorial interpretations of their vanishing. We also study tight distance-regular graphs of diameter 3 and 4. In the case of diameter 3, tight graphs are precisely the Taylor graphs. In the case of antipodal distance-regular graphs of diameter 4, tight graphs are precisely the graphs for which the Krein parameter q(11)(4) vanishes. (C) 2002 Elsevier Science B.V. All rights reserved.
引用
收藏
页码：181 / 202
页数：22
相关论文
共 50 条
  • [41] GRAPHS OF DIAMETER 3 WITH THE MINIMUM NUMBER OF EDGES
    FUREDI, Z
    GRAPHS AND COMBINATORICS, 1990, 6 (04) : 333 - 337
  • [42] On mixed radial Moore graphs of diameter 3
    Ceresuela, J. M.
    Lopez, N.
    Chemisana, D.
    DISCRETE MATHEMATICS, 2023, 346 (09)
  • [43] On Bipartite Graphs of Diameter 3 and Defect 2
    Delorme, Charles
    Jorgensen, Leif K.
    Miller, Mirka
    Pineda-Villavicencio, Guillermo
    JOURNAL OF GRAPH THEORY, 2009, 61 (04) : 271 - 288
  • [44] DISTANCE REGULAR GRAPHS OF DIAMETER-3 AND STRONGLY REGULAR GRAPHS
    BROUWER, AE
    DISCRETE MATHEMATICS, 1984, 49 (01) : 101 - 103
  • [45] On a Family of 4-Critical Graphs with Diameter Three
    Barioli, Francesco
    Loizeaux, Marc
    van der Merwe, Lucas
    ARS COMBINATORIA, 2012, 105 : 83 - 93
  • [46] Forcing large tight components in 3-graphs
    Georgakopoulos, Agelos
    Haslegrave, John
    Montgomery, Richard
    EUROPEAN JOURNAL OF COMBINATORICS, 2019, 77 : 57 - 67
  • [47] Edge number of 3-connected diameter 3 graphs
    Tsai, MC
    Fu, HL
    I-SPAN 2004: 7TH INTERNATIONAL SYMPOSIUM ON PARALLEL ARCHITECTURES, ALGORITHMS AND NETWORKS, PROCEEDINGS, 2004, : 364 - 367
  • [48] Two new infinite families of arc-transitive antipodal distance-regular graphs of diameter three with related to groups and
    Tsiovkina, L. Yu
    JOURNAL OF ALGEBRAIC COMBINATORICS, 2015, 41 (04) : 1079 - 1087
  • [49] Average Shortest Path Length of Graphs of Diameter 3
    Shimizu, Nobutaka
    Mori, Ryuhei
    2016 TENTH IEEE/ACM INTERNATIONAL SYMPOSIUM ON NETWORKS-ON-CHIP (NOCS), 2016,
  • [50] THE GENERALIZED S-GRAPHS OF DIAMETER-3
    MENG, JX
    DISCRETE MATHEMATICS, 1995, 140 (1-3) : 95 - 106
12345