GENREG swMATH ID: 26671 Software Authors: Meringer, Markus Description: Fast generation of regular graphs and construction of cages. The construction of complete lists of regular graphs up to isomorphism is one of the oldest problems in constructive combinatorics. In this article an efficient algorithm to generate regular graphs with a given number of vertices and vertex degree is introduced. The method is based on orderly generation refined by criteria to avoid isomorphism checking and combined with a fast test for canonicity. The implementation allows computing even large classes of graphs, like construction of the 4-regular graphs on 18 vertices and, for the first time, the 5-regular graphs on 16 vertices. Also in cases with given girth, some remarkable results are obtained. For instance, the 5-regular graphs with girth 5 and minimal number of vertices were generated in less than 1,h. There exist exactly four (5,,5)-cages. Homepage: http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html Keywords: cage; orderly generation; regular graphs; isomorphism Related Software: nauty; House of Graphs; Traces; snarkhunter; plantri; OEIS; GenHypohamiltonian; GAP; SageMath; Boost; bliss; GraPHedron; CaGe; WolframAlpha; Groups & Graphs; GenerateUHG; MathOverflow; SnapPy; JAS; Boost C++ Libraries Cited in: 61 Documents all top 5 Cited by 108 Authors 7 Araujo-Pardo, Gabriela 7 Brinkmann, Gunnar 6 Balbuena, Camino 6 Goedgebeur, Jan 4 Haythorpe, Michael 4 Zamfirescu, Carol T. 3 Abreu, Marién 3 Ezhov, Vladimir Vladimirovich 3 Filar, Jerzy A. 3 Labbate, Domenico 2 Fowler, Patrick W. 2 McKay, Brendan D. 2 Pisanski, Tomaž 2 Richter, Hendrik 2 Rossomakhine, Serguei 1 Abajo, Encarnación 1 Abrosimov, Mikhail Borisovich 1 Balardin, Joana Bisol 1 Bendala, M. 1 Boben, Marko 1 Bokal, Drago 1 Bokowski, Jürgen G. 1 Brijder, Robert 1 Cakiroglu, Sera Aylin 1 Chiers, Sara 1 Clancy, Kieran 1 Coolsaet, Kris 1 Demongeot, Jacques 1 Dybizbański, Janusz 1 Elena, Adrien 1 Fabrici, Igor 1 Feria-Purón, Ramiro 1 Fujita, André 1 Funk, Martin J. 1 Gauci, John Baptist 1 Graovac, Ante 1 Gray, Ian D. 1 Grünbaum, Branko 1 Grünewald, Stefan 1 Gu, Qianping 1 Harmuth, Thomas 1 Haymaker, Kathryn 1 Haythorpe, Micheal 1 Héger, Tamás 1 Heidemeier, Oliver 1 Hoppe, Travis 1 Hougardy, Stefan 1 Jajcay, Robert 1 Kamil, Ikhab AAbdzhuldzhabbar Kamil 1 Kaski, Petteri 1 Kasyoki, Donnie 1 Koledin, Tamara 1 Köthnig, Ivo 1 Larrion, Francisco 1 Lauri, Juho 1 Lin, Xiaohui 1 Lobov, Aleksandr Andreevich 1 Logan, Adam 1 Lucas, Stephen K. 1 Máčajová, Edita 1 MacDougall, James A. 1 Madaras, Tomáš 1 Marušič, Dragan 1 Mazák, Ján 1 Meersman, Barbara 1 Meringer, Markus 1 Mitillos, Christodoulos 1 Mukkamala, Padmini 1 Nedela, Roman 1 Newcombe, Alex 1 Nguyen, Giang Thu 1 Noual, Mathilde 1 Ochem, Pascal 1 Oleche, Paul O. 1 O’Pella, Justin 1 Orbanić, Alen 1 Östergård, Patric R. J. 1 Pálvölgyi, Dömötör 1 Pegg, Ed jun. 1 Petrone, Anna 1 Pineda-Villavicencio, Guillermo 1 Pinlou, Alexandre 1 Pizanã, Miguel Algel 1 Qiao, Jing 1 Raiman, Tom 1 Samodivkin, Vladimir D. 1 Sato, João Ricardo 1 Schauz, Uwe 1 Schewe, Lars 1 Sciriha, Irene 1 Sené, Sylvain 1 Sikora, Adam S. 1 Škoviera, Martin 1 Stanić, Zoran 1 Sudani, Hayder Hussein Karim 1 Szepietowski, Andrzej 1 Takahashi, Daniel Yasumasa 1 Thuderoz, Florence 1 Timková, Mária 1 Traldi, Lorenzo ...and 8 more Authors all top 5 Cited in 37 Serials 11 Discrete Mathematics 7 Discrete Applied Mathematics 3 Graphs and Combinatorics 2 Mathematics of Computation 2 European Journal of Combinatorics 2 Linear Algebra and its Applications 2 The Electronic Journal of Combinatorics 2 Discussiones Mathematicae. Graph Theory 1 Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Biology 1 Applied Mathematics and Computation 1 Journal of Combinatorial Theory. Series B 1 Journal of Graph Theory 1 Journal of Number Theory 1 Mathematics of Operations Research 1 Networks 1 Note di Matematica 1 Computers & Operations Research 1 Journal of Parallel and Distributed Computing 1 Computational Statistics and Data Analysis 1 Journal of Knot Theory and its Ramifications 1 The Australasian Journal of Combinatorics 1 Experimental Mathematics 1 Journal of Combinatorial Designs 1 Journal of Mathematical Chemistry 1 Discrete Mathematics and Theoretical Computer Science. DMTCS 1 MATCH - Communications in Mathematical and in Computer Chemistry 1 Journal of Discrete Algorithms 1 Ars Mathematica Contemporanea 1 Games 1 Statistics and Computing 1 International Journal of Group Theory 1 Journal of Theoretical Biology 1 Journal of Algebra, Combinatorics, Discrete Structures and Applications 1 DML. Discrete Mathematics Letters 1 The Art of Discrete and Applied Mathematics 1 Prikladnaya Diskretnaya Matematika all top 5 Cited in 13 Fields 54 Combinatorics (05-XX) 5 Computer science (68-XX) 4 Geometry (51-XX) 4 Biology and other natural sciences (92-XX) 3 Convex and discrete geometry (52-XX) 2 Number theory (11-XX) 2 Statistics (62-XX) 2 Operations research, mathematical programming (90-XX) 1 Algebraic geometry (14-XX) 1 Group theory and generalizations (20-XX) 1 Manifolds and cell complexes (57-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year