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

Abstract

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 S_p 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≤r<m. G _m,n is just the Hasse 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 Rö] and in general in [Bu Gr La].