Arrowhead and Diamond Diameters

Abstract

{\em Arrowhead} and {\em diamond} are two hierarchical Cayley graphs defined on the triangular grid. In their undirected version, they are isomorphic and merely define two distinct representations of the same graph. This paper gives the expression of their diameter, in the oriented and non--oriented case. It also displays the full distribution of antipodals.

17 pages, 7 figures