The Biggs-Smith graph is cubic symmetric graph 
on 102 vertices and 153 edges.
It is illustrated above in a number of embeddings.
It is implemented in the Wolfram Language as GraphData["BiggsSmithGraph"].
It is 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).
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) and none of which have bilteral symmetry
(E. Weisstein, Jan. 3, 2026). One such LCF
notation (of length 102) is given by [16, 24, -38, 17, 34, 48, -19, 41, -35,
47, -20, 34, -36, 21, 14, 48, -16, -36, -43, 28, -17, 21, 29, -43, 46, -24, 28, -38,
-14, -50, -45, 21, 8, 27, -21, 20, -37, 39, -34, -44, -8, 38, -21, 25, 15, -34, 18,
-28, -41, 36, 8, -29, -21, -48, -28, -20, -47, 14, -8, -15, -27, 38, 24, -48, -18,
25, 38, 31, -25, 24, -46, -14, 28, 11, 21, 35, -39, 43, 36, -38, 14, 50, 43, 36,
-11, -36, -24, 45, 8, 19, -25, 38, 20, -24, -14, -21, -8, 44, -31, -38, -28, 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 
.
