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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 ...

Let G be a simple connected graph, and take 0<=i<=d(G), where d(G) is the graph diameter. Then G has global parameters c_i (respectively a_i, b_i) if the number of vertices ...

The Leonard graph is a distance-regular graph on 288 vertices (Brouwer et al. 1989, p. 369) with intersection array {12,11,10,7;1,2,5,12}. It is however not ...

The stacked book graph of order (m,n) is defined as the graph Cartesian product S_(m+1) square P_n, where S_m is a star graph and P_n is the path graph on n nodes. It is ...

The (m,q)-Ustimenko graph is the distance-1 or distance-2 graph of the dual polar graph on [C_m(q)] (Brouwer et al. 1989, p. 279). The Ustimenko graph with parameters m and q ...

The depth of a box is the horizontal distance from front to back (usually not necessarily defined to be smaller than the width, the horizontal distance from side to side).

The diameter of a circle is the distance from a point on the circle to a point pi radians away, and is the maximum distance from one point on a circle to another. The ...

The Hadwiger-Nelson problem asks for the chromatic number of the plane, i.e., the minimum number of colors needed to color the plane if no two points at unit distance one ...

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

The width of a box is the horizontal distance from side to side (usually defined to be greater than the depth, the horizontal distance from front to back).