Geodesic
Lobe, edge, and arc transitivity of graphs of connectivity 1
Ars Mathematica Contemporanea, Tome 17 (2019) no. 2, pp. 581-589.

Voir la notice de l'article provenant de la source Ars Mathematica Contemporanea website

We give necessary and sufficient conditions for lobe-transitivity of locally finite and locally countable graphs whose connectivity equals 1. We show further that, given any biconnected graph Λ and a “code” assigned to each orbit of Aut(Λ), there exists a unique lobe-transitive graph Γ of connectivity 1 whose lobes are copies of Λ and is consistent with the given code at every vertex of Γ. These results lead to necessary and sufficient conditions for a graph of connectivity 1 to be edge-transitive and to be arc-transitive. Countable graphs of connectivity 1 the action of whose automorphism groups is, respectively, vertex-transitive, primitive, regular, Cayley, and Frobenius had been previously characterized in the literature.
DOI : 10.26493/1855-3974.1866.fd9
Keywords: Lobe, lobe-transitive, edge-transitive, orbit, connectivity 
@article{10_26493_1855_3974_1866_fd9,
     author = {Jack E. Graver and Mark E. Watkins},
     title = {Lobe, edge, and arc transitivity of graphs of connectivity 1},
     journal = {Ars Mathematica Contemporanea},
     pages = {581--589},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2019},
     doi = {10.26493/1855-3974.1866.fd9},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1866.fd9/}
}
TY  - JOUR
AU  - Jack E. Graver
AU  - Mark E. Watkins
TI  - Lobe, edge, and arc transitivity of graphs of connectivity 1
JO  - Ars Mathematica Contemporanea
PY  - 2019
SP  - 581
EP  - 589
VL  - 17
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1866.fd9/
DO  - 10.26493/1855-3974.1866.fd9
LA  - en
ID  - 10_26493_1855_3974_1866_fd9
ER  - 
%0 Journal Article
%A Jack E. Graver
%A Mark E. Watkins
%T Lobe, edge, and arc transitivity of graphs of connectivity 1
%J Ars Mathematica Contemporanea
%D 2019
%P 581-589
%V 17
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1866.fd9/
%R 10.26493/1855-3974.1866.fd9
%G en
%F 10_26493_1855_3974_1866_fd9
Jack E. Graver; Mark E. Watkins. Lobe, edge, and arc transitivity of graphs of connectivity 1. Ars Mathematica Contemporanea, Tome 17 (2019) no. 2, pp. 581-589. doi : 10.26493/1855-3974.1866.fd9. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1866.fd9/

Cité par Sources :