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The (m,n)-tadpole graph, also called a dragon graph (Truszczyński 1984) or kite graph (Kim and Park 2006), is the graph obtained by joining a cycle graph C_m to a path graph ...

The m×n rook graph (confusingly called the m×n grid by Brouwer et al. 1989, p. 440) and also sometimes known as a lattice graph (e.g., Brouwer) is the graph Cartesian product ...

The Shrikhande graph is a strongly regular graph on 16 nodes. It is cospectral with the rook graph L_(4,4), so neither of the two is determined by spectrum. The Shrikhande ...

The Petersen graph is the cubic graph on 10 vertices and 15 edges which is the unique (3,5)-cage graph (Harary 1994, p. 175), as well as the unique (3,5)-Moore graph. It can ...

There are a number of hypotraceable and hypohamiltonian graphs associated with Carsten Thomassen. These graphs, illustrated above, are implemented in the Wolfram Language as ...

Let A^~, B^~, ... be operators. Then the commutator of A^~ and B^~ is defined as [A^~,B^~]=A^~B^~-B^~A^~. (1) Let a, b, ... be constants, then identities include [f(x),x] = 0 ...

A cyclotomic field Q(zeta) is obtained by adjoining a primitive root of unity zeta, say zeta^n=1, to the rational numbers Q. Since zeta is primitive, zeta^k is also an nth ...

An integer d is a fundamental discriminant if it is not equal to 1, not divisible by any square of any odd prime, and satisfies d=1 (mod 4) or d=8,12 (mod 16). The function ...

A bicubic graph is a bipartite cubic graph. Tutte (1971) conjectured that all 3-connected bicubic graphs are Hamiltonian (the Tutte conjecture), but a number of bicubic ...

A fan graph F_(m,n) is defined as the graph join K^__m+P_n, where K^__m is the empty graph on m nodes and P_n is the path graph on n nodes. The case m=1 corresponds to the ...