Bounding the Valency of Polygonal Graphs With Odd Girth
Manley Perkel · Canadian Journal of Mathematics · 1979
In this paper we investigate the action of finite groups G on finite polygonal graphs. The notion of a polygonal graph was introduced in [17]: A polygonal graph is a pair ( , ) consisting of a graph which is regular, connected and has girth m for some m ≧ 3, and a set of m-gons of such that every 2-claw of is contained in an unique element of (See Section 2 for the définitions of the terms used here.) If is the set of all m-gons of , so that there is in an unique m-gon on every one of its 2-claws, then we write for ( , ) and call a strict polygonal graph. If we wish to emphasize the integer m, then we call ( , ) an m-gon-graph (respectively, a strict m-gon-graph).