Geodesic
On narrow hexagonal graphs with a 3-homogeneous suborbit
Journal of Algebraic Combinatorics, Tome 13 (2001) no. 3, pp. 257-273.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A connected graph of girth $mge$ 3 is called a polygonal graph if it contains a set of $m$-gons such that every path of length two is contained in a unique element of the set. In this paper we investigate polygonal graphs of girth 6 or more having automorphism groups which are transitive on the vertices and such that the vertex stabilizers are 3-homogeneous on adjacent vertices. We previously showed that the study of such graphs divides naturally into a number of substantial subcases. Here we analyze one of these cases and characterize the $k$-valent polygonal graphs of girth 6 which have automorphism groups transitive on vertices, which preserve the set of special hexagons, and which have a suborbit of size $k - 1$ at distance three from a given vertex.
Keywords: polygonal graph, automorphism group, 3-homogeneous suborbit 
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     title = {On narrow hexagonal graphs with a 3-homogeneous suborbit},
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Perkel, Manley; Praeger, Cheryl E.; Weiss, Richard. On narrow hexagonal graphs with a 3-homogeneous suborbit. Journal of Algebraic Combinatorics, Tome 13 (2001) no. 3, pp. 257-273. http://geodesic.mathdoc.fr/item/JAC_2001__13_3_a3/