A NOTE ON THE EXTENDABILITY OF AN ISOMORPHISM OF SUBGRAPHS OF A GRAPH TO AN AUTOMORPHISM OF THE GRAPH

Результат исследований: Вклад в журналСтатья

Аннотация

Let Г be an undirected connected locally finite graph such that its automorphism group is vertex-transitive and has finite vertex stabilizers. For a vertex v of Г and a non-negative integer n, let <BГ(v,n)>Г denote the subgraph of Г generated by the ball BГ(v,n) of radius n with center v. We prove that there exists a non-negative integer c (depending only on Г) such that, for any vertices x and y of Г and any non-negative integer r, if an isomorphism of <BГ(x,r)>Г onto <BГ(y,r)>Г can be extended to an isomorphism of <BГ(x,r+c)>Г onto <BГ(y,r+c)>Г, then it can also be extended to an automorphism of Г. Furthermore, we give a ``formula'' for c. In such a form the result can also be of interest for finite graphs Г.
Язык оригиналаАнглийский
ЖурналТруды института математики и механики УрО РАН
Том18
Номер выпуска3
СостояниеОпубликовано - 2012

    Fingerprint

ГРНТИ

  • 27.17.00 Алгебра

Уровень публикации

  • Перечень ВАК

Цитировать