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A quintic symmetric graph is a quintic graph (i.e., regular of degree 5) that is also symmetric. Since quintic graphs exist only on an even number of nodes, so do symmetric ...

A K-rational point is a point (X,Y) on an algebraic curve f(X,Y)=0, where X and Y are in a field K. For example, rational point in the field Q of ordinary rational numbers is ...

The regular octagon is the regular polygon with eight sides, as illustrated above. The inradius r, circumradius R, and area A of the regular octagon can be computed directly ...

The study of manifolds having a complete Riemannian metric. Riemannian geometry is a general space based on the line element ds=F(x^1,...,x^n;dx^1,...,dx^n), with F(x,y)>0 ...

A septic graph is a regular graph of degree seven. The numbers of (not necessarily connected) simple septic graphs on n=8, 10, 12, ... vertices are 1, 5, 1547, 21609301, ...

The general sextic equation x^6+a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0=0 can be solved in terms of Kampé de Fériet functions, and a restricted class of sextics can be solved in ...

A sextic graph is a regular graph of degree six. The numbers of simple sextic graphs on n=7, 8, ... nodes are 1, 1, 4, 21, 266, 7846, 367860, ... (OEIS A006822). Examples are ...

Seymour conjectured that a graph G of order n with minimum vertex degree delta(G)>=kn/(k+1) contains the kth graph power of a Hamiltonian cycle, generalizing Pósa's ...

There are at least two Siegel's theorems. The first states that an elliptic curve can have only a finite number of points with integer coordinates. The second states that if ...

The Sombor energy of a graph is defined as the graph energy of its Sombor matrix, i.e., the sum of the absolute values of the eigenvalues of its Sombor matrix.