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The Balaban 11-cage is the unique 11-cage graph, derived via a tree excision from the 12-cage graph by Balaban (1973) and proven unique by McKay and Myrvold in 2003. It is ...

A n-crossed prism graph for positive even n (a term introduced here for the first time), is a graph obtained by taking two disjoint cycle graphs C_n and adding edges ...

The average distance between two points chosen at random inside a unit cube (the n=3 case of hypercube line picking), sometimes known as the Robbins constant, is Delta(3) = ...

Let A be an edge cut of a connected graph G. Then the cyclic edge connectivity lambda_c(G) is the size of a smallest cyclic edge cut, i.e., a smallest edge cut A such that ...

A double sum is a series having terms depending on two indices, sum_(i,j)b_(ij). (1) A finite double series can be written as a product of series ...

The E graph is the tree on 6 vertices illustrated above. It is isomorphic to the (3,2)-firecracker graph and 3-centipede graph. It is implemented in the Wolfram Language as ...

A fixed point is a point that does not change upon application of a map, system of differential equations, etc. In particular, a fixed point of a function f(x) is a point x_0 ...

The floor function |_x_|, also called the greatest integer function or integer value (Spanier and Oldham 1987), gives the largest integer less than or equal to x. The name ...

The isogonal conjugate X^(-1) of a point X in the plane of the triangle DeltaABC is constructed by reflecting the lines AX, BX, and CX about the angle bisectors at A, B, and ...

A manifold is a topological space that is locally Euclidean (i.e., around every point, there is a neighborhood that is topologically the same as the open unit ball in R^n). ...