Aut G m,n for the Hasse Graph G m,n of the Subword Poset B m,n of an m-Ary Cyclic Word of Length n

There exists a rich literature on automorphism groups for (undirected) graphs. This subject is specially developed for distance transitive graphs (one of them is the n-cube). We consider here a non distance transitive graph G m,n obtained from the hypercube by identifying some of its vertices and we charcaterise its automorphism group in terms of Sp the symmetric group on p elements. Starting point for this study has been when investigating the poset B m,n of all sub-words from a given word of length n: $${{\text{u}}_{\text{m,n}}}=....\left( \text{m-1} \right)01....\left( \text{m-1} \right) 01....\left( \text{m-1} \right)01...\left( \text{r-1} \right),$$ where n=qm+r with 0≤rHasse graph of B m,n . G m,n for n≤m is an n-dimensional cube Q n . The automorphism group of B m,n (as a poset) were characterised for m=2 in [Bu Fr Ro] and in general in [Bu Gr La].