Recurrence Relations and Hilbert Series of the Monoid Associated with Star Topology

Affine monoids are the considered as natural discrete analogues of the finitely generated cones. The interconnection between these two objects has been an active area of research since last decade. Star network is one of the most common in computer network topologies. In this work, we study star topology and associate a Coxeter structure of affine type on it. We find a recurrence relation and the Hilbert series of the associated right-angled monoid . We observe that the growth rate of the monoid is unbounded.