The Biggs-Smith graph is cubic symmetric graph 
on 102 vertices and 153 edges
that is also distance-regular with intersection
array 
and distance-transitive.
It is known to be uniquely determined by its graph spectrum (van Dam and Haemers 2003). Its automorphism group is of order 2448 (Royle).
It is implemented in the Wolfram Language as GraphData["BiggsSmithGraph"].
The Biggs-Smith graph is an order-17 graph expansion of the H graph with step offsets 3, 5, 6, and 7 (where
these are a different set of steps from those reported by Biggs 1993, p. 147).
It is therefore one of only two cubic symmetric H graphs (the other being 
).
The Biggs-Smith graph is a unit-distance graph, as are all cubic symmetric H-, I-, and Y-graphs (E. Gerbracht, pers. comm., Jan. 2010).
The Biggs-Smith graph has 
distinct (directed) Hamiltonian cycles which correspond
to 890 distinct LCF notations, all of which are of
order 1 (E. Weisstein, May 30, 2008). One such LCF
notation (of length 102) is given by [16, 24, 
, 17, 34, 48, 
, 41, 
, 47, 
, 34, 
, 21, 14, 48, 
, 
, 
, 28, 
, 21, 29, 
, 46, 
, 28, 
, 
, 
, 
, 21, 8, 27, 
, 20, 
, 39, 
, 
, 
, 38, 
, 25, 15, 
, 18, 
, 
, 36, 8, 
, 
, 
, 
, 
, 
, 14, 
, 
, 
, 38, 24, 
, 
, 25, 38, 31, 
, 24, 
, 
, 28, 11, 21, 35, 
, 43, 36, 
, 14, 50, 43, 36, 
, 
, 
, 45, 8, 19, 
, 38, 20, 
, 
, 
, 
, 44, 
, 
, 
, 37].
The plots above show the adjacency, incidence, and distance matrices of the graph.
The bipartite double graph and double cover of the Biggs-Smith graph is the cubic symmetric
graph 
.
