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A graph G is said to be disconnected if it is not connected, i.e., if there exist two nodes in G such that no path in G has those nodes as endpoints. The numbers of ...

The partial differential equation u_t+u_(xxx)-6uu_x=0 (1) (Lamb 1980; Zwillinger 1997, p. 175), often abbreviated "KdV." This is a nondimensionalized version of the equation ...

The Hall-Janko near octagon, also known as the Cohen-Tits near octagon, is a weakly regular graph on 315 vertices with parameters (n,k,lambda,mu)=(315,(10),(1),(0,1)). It is ...

A vertex cut, also called a vertex cut set or separating set (West 2000, p. 148), of a connected graph G is a subset of the vertex set S subset= V(G) such that G-S has more ...

The numbers of positive definite n×n matrices of given types are summarized in the following table. For example, the three positive eigenvalues 2×2 (0,1)-matrices are [1 0; 0 ...

The shortest circular sequence of length sigma^n such that every string of length n on the alphabet a of size sigma occurs as a contiguous subrange of the sequence described ...

The hexacode graph is the incidence graph of the unique symmetric transversal design STD_2[6;3]. It is also a bipartite (0,2)-graph. The hexacode graph is a ...

The Soicher graphs are three distance-regular graphs on 5346, 486, and 315 vertices, respectively. The first two are also distance-transitive but the third is not. The second ...

A strongly binary tree is a rooted tree for which the root is adjacent to either zero or two vertices, and all non-root vertices are adjacent to either one or three vertices ...

Define a carefree couple as a pair of positive integers (a,b) such that a and b are relatively prime (i.e., GCD(a,b)=1) and a is squarefree. Similarly, define a strongly ...