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 .