On arrowhead and diamond diameters

Désérable, Dominique (National Institute of Applied Sciences, Rennes, France)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 13, No 1 (2025): Electronic Journal of Graph Theory and Applications

Arrowhead and diamond form a family of 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. This family could appear as a promising topology for Network–on–Chip architectures.