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The Egawa graph with parameters (p,s) is a distance-regular but not distance-transitive graph on 16^p4^s nodes. These graphs generalize the Doob graphs and give (s,4)-Hamming ...

The Ljubljana graph is a graph on 112 vertices that is the third smallest cubic semisymmetric graph. It was discovered by Brouwer et al. (1993) and rediscovered by Conder et ...

For a permutation alpha in the symmetric group S_p, the alpha-permutation graph of a labeled graph G is the graph union of two disjoint copies of G (say, G_1 and G_2), ...

Define a = d(u,v)d(w,x) (1) b = d(u,w)d(v,x) (2) c = d(u,x)d(v,w), (3) where u, v, w, and x are vertices of a graph and d(i,j) is the graph distance between vertices i and j. ...

The n-path complement graph P^__n is the graph complement of the path graph P_n. The first few are illustrated above. Since P_4 is self-complementary, P^__4 is isomorphic to ...

A Mongolian tent graph is defined as the graph obtained from the grid graph P_m square P_n for odd n by adding an extra vertex above the graph and joining every other vertex ...

The Dejter graph is a weakly regular graph on 112 vertices and 336 edges with regular paremeters (nu,k,lambda,mu)=(112,6,0,(0,1,2)). It can be obtained by deleting a copy of ...

The Sims graph is a distance-transitive graph on 352 vertices (Brouwer et al. 1989, p. 370).

The Van Lint-Schrijver Graph graph is a weakly regular Hamiltonian graph on 162 vertices with parameters (nu,k,lambda,mu)=(162,(6),(0),(0,1)). It is distance-regular with ...

The m×n queen graph Q_(m,n) is a graph with mn vertices in which each vertex represents a square in an m×n chessboard, and each edge corresponds to a legal move by a queen. ...