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A number of strongly regular graphs of several types derived from combinatorial design were identified by Goethals and Seidel (1970). Theorem 2.4 of Goethals and Seidel ...

The gonality (also called divisorial gonality) gon(G) of a (finite) graph G is the minimum degree of a rank 1 divisor on that graph. It can be thought of as the minimum ...

There are a number of formulas variously known as Hurwitz's formula. The first is zeta(1-s,a)=(Gamma(s))/((2pi)^s)[e^(-piis/2)F(a,s)+e^(piis/2)F(-a,s)], where zeta(z,a) is a ...

A set n distinct numbers taken from the interval [1,n^2] form a magic series if their sum is the nth magic constant M_n=1/2n(n^2+1) (Kraitchik 1942, p. 143). If the sum of ...

Dirac (1952) proved that if the minimum vertex degree delta(G)>=n/2 for a graph G on n>=3 nodes, then G contains a Hamiltonian cycle (Bollobás 1978, Komlós et al. 1996). In ...

A quasi-cubic graph is a quasi-regular graph, i.e., a graph such that degree of every vertex is the same delta except for a single vertex whose degree is Delta=delta+1 ...

A rational amicable pair consists of two integers a and b for which the divisor functions are equal and are of the form sigma(a)=sigma(b)=(P(a,b))/(Q(a,b))=R(a,b), (1) where ...

Unlike quadratic, cubic, and quartic polynomials, the general quintic cannot be solved algebraically in terms of a finite number of additions, subtractions, multiplications, ...

An arc-transitive graph, sometimes also called a flag-transitive graph, is a graph whose graph automorphism group acts transitively on its graph arcs (Godsil and Royle 2001, ...

The McLaughlin graph is a 112-regular graph on 275 nodes and 15400 edges that can be constructed from the Witt design. It is distance-regular with intersection array ...