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Vertex-transitive graphs and their arc-typesConder, Marston D. E. ; Pisanski, Tomaž ; Žitnik, ArjanaNaj bo ▫$X$▫ končen vozliščno-tranzitiven graf valence ▫$d$▫, in naj bo ▫$A$▫ polna grupa avtomorfizmov grafa ▫$X$▫. Potem je ločni tip grafa ▫$X$▫ definiran v smislu velikosti orbit stabilizatorja ... ▫$A_v$▫ danega vozlišča ▫$v$▫ na množici lokov incidentnih z ▫$v$▫. Za takšno orbito pravimo, da je sebi-prirejena, če je vsebovana v orbiti ▫$\Delta$▫ grupe ▫$A$▫ na množici vseh takšnih lokov grafa ▫$X$▫, za katere je orbita ▫$\Delta$▫ zaprta za obračanje lokov. Ločni tip grafa ▫$X$▫ je tedaj razčlenitev števila ▫$d$▫ v vsoto ▫$n_1 + n_2 + \dots + n_t + (m_1 + m_1) + (m_2 + m_2) + \dots + (m_s + m_s)$▫, kjer so ▫$n_1, n_2, \dots, n_t$▫ velikosti sebi-prirejenih orbit, ▫$m_1,m_1, m_2,m_2, \dots, m_s,m_s$▫, ms pa so velikosti sebi-neprirejenih orbit, v padajočem redu. V tem članku najdemo ločne tipe več družin grafov. Pokažemo tudi, da je ločni tip kartezičnega produkta dveh "tujih si" grafov naravna vsota njunih ločnih tipov. Potem na podlagi teh opažanj pokažemo, da je, z izjemo ▫$1+1$▫ in ▫$(1+1)$▫, vsaka particija, kot je definirana zgoraj, realizabilna, v tem smislu, da obstaja vsaj en vozliščno-tranzitiven graf z dano razčlenitvijo kot svojim ločnim tipom.Source: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 12, no. 2, 2017, str. 383-413)Type of material - article, component part ; adult, seriousPublish date - 2017Language - englishCOBISS.SI-ID - 18064217
Author
Conder, Marston D. E. |
Pisanski, Tomaž |
Žitnik, Arjana
Topics
tip simetrije |
vozliščno tranzitiven graf |
ločno trazitiven graf |
Cayleyjev graf |
kartezični produkt |
krovni graf |
symmetry type |
vertex-transitive graph |
arc-transitive graph |
Cayley graph |
cartesian product |
covering graph
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Conder, Marston D. E. | ![]() |
Pisanski, Tomaž | 01941 |
Žitnik, Arjana | 14273 |
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