Lobe, edge, and arc transitivity of graphs of connectivity 1
Graver, Jack E., 1935- ; Watkins, Mark E., 1937-2024
Podamo potrebne in zadostne pogoje za reženjsko tranzitivnost lokalno končnih in lokalno števnih grafov, katerih povezanost je enaka 1. Nadalje pokažemo, da za vsak bipovezan graf ▫$\Lambda$▫ in ..."kodo", prirejeno vsaki orbiti grupe Aut(▫$\Lambda$▫), obstaja en sam reženjsko tranzitiven graf ▫$\Gamma$▫ s povezanostjo 1, katerega režnji so kopije grafa ▫$\Lambda$▫ in je konsistenten z dano kodo v vsakem vozlišču grafa ▫$\Gamma$▫. Ti rezultati vodijo k potrebnim in zadostnim pogojem za to, da je graf s povezanostjo 1 povezavno tranzitiven in ločno tranzitiven. Števni grafi s povezanostjo 1, za katere je delovanje njihovih grup avtomorfizmov vozliščno tranzitivno, primitivno, regularno, Cayleyjevo ali Frobeniusovo, so bili v literaturi karakterizirani že prej.
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