Generating connected and 2-edge connected graphs

被引：0
|
作者：
Doppler Institute and Department of Mathematics, FNSPE, Czech Technical University, Trojanova 13, 120 00 Praha 2, Czech Republic [1 ]
不详 [2 ]
机构：
来源：
J. Graph Algorithms and Appl. | 2009年 / 2卷 / 251-281期
关键词：
Graph theory - Graphic methods;
D O I：
10.7155/jgaa.00187
中图分类号：
O144 [集合论]; O157 [组合数学（组合学）];
学科分类号：
070104 ;
摘要：
We focus on the algorithm underlying the main result of [6]. This is an algebraic formula to generate all connected graphs in a recursive and effcient manner. The key feature is that each graph carries a scalar factor given by the inverse of the order of its group of automorphisms. In the present paper, we revise that algorithm on the level of graphs. Moreover, we extend the result subsequently to further classes of connected graphs, namely, 2-edge connected, simple and loopless graphs. Our method con- sists of basic graph transformations only.
引用
收藏
相关论文
共 50 条
  • [31] Improving on the 1.5-approximation of a smallest 2-edge connected spanning subgraph
    Cheriyan, J
    Sebo, A
    Szigeti, Z
    SIAM JOURNAL ON DISCRETE MATHEMATICS, 2001, 14 (02) : 170 - 180
  • [32] EDGE FORWARDING INDICES OF 2-EDGE-CONNECTED GRAPHS
    Cai Maocheng (Institute of Systems Science
    新疆大学学报(自然科学版), 1990, (04) : 11 - 13
  • [33] Generating random connected planar graphs
    Griffith, Daniel A.
    GEOINFORMATICA, 2018, 22 (04) : 767 - 782
  • [34] Generating random connected planar graphs
    Daniel A. Griffith
    GeoInformatica, 2018, 22 : 767 - 782
  • [35] An improved approximation algorithm for minimum size 2-edge connected spanning subgraphs
    Cheriyan, J
    Sebö, A
    Szigeti, Z
    INTEGER PROGRAMMING AND COMBINATORIAL OPTIMIZATION, 1998, 1412 : 126 - 136
  • [36] Finding 2-Edge and 2-Vertex Strongly Connected Components in Quadratic Time
    Henzinger, Monika
    Krinninger, Sebastian
    Loitzenbauer, Veronika
    AUTOMATA, LANGUAGES, AND PROGRAMMING, PT I, 2015, 9134 : 713 - 724
  • [37] 2-Edge Connectivity in Directed Graphs
    Georgiadis, Loukas
    Italiano, Giuseppe F.
    Laura, Luigi
    Parotsidis, Nikos
    ACM TRANSACTIONS ON ALGORITHMS, 2016, 13 (01)
  • [38] Average connectivity of minimally 2-connected graphs and average edge-connectivity of minimally 2-edge-connected graphs
    Casablanca, Rocio M.
    Mol, Lucas
    Oellermann, Ortrud R.
    DISCRETE APPLIED MATHEMATICS, 2021, 289 : 233 - 247
  • [39] Finding 2-edge and 2-vertex strongly connected components in quadratic time
    20155101705918
    (1) University of Vienna, Vienna, Austria, 1600, ERATO Kawarabayashi Large Graph Project; MEXT Grant-in-Aid for Scientific Research on Innovative Areas: Exploring the Limits of Computation; Research Institute for Mathematical Sciences; Tateisi Science and Technology Foundation (Springer Verlag):
  • [40] MAINTENANCE OF 2-EDGE-CONNECTED AND 3-EDGE-CONNECTED COMPONENTS OF GRAPHS .1.
    LAPOUTRE, JA
    VANLEEUWEN, J
    OVERMARS, MH
    DISCRETE MATHEMATICS, 1993, 114 (1-3) : 329 - 359
12345