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An integral embedding of a graph, not to be confused with an integral graph, is a graph drawn such that vertices are distinct points and all graph edges have integer lengths. ...

The maximum leaf number l(G) of a graph G is the largest number of tree leaves in any of its spanning trees. (The corresponding smallest number of leaves is known as the ...

The multicomputational paradigm is a generalization of the computational paradigm to many computational threads of time. In the ordinary computational paradigm, time ...

A nut graph is a graph on n>=2 vertices with adjacency matrix A such that A has matrix rank 1 and contains no 0 element (Sciriha 1998, 2008; Sciriha and Gutman, 1998; and ...

The mathematical study of combinatorial objects in which a certain degree of order must occur as the scale of the object becomes large. Ramsey theory is named after Frank ...

For a given positive integer n, does there exist a weighted tree with n graph vertices whose paths have weights 1, 2, ..., (n; 2), where (n; 2) is a binomial coefficient? ...

The number of colors sufficient for map coloring on a surface of genus g is given by the Heawood conjecture, chi(g)=|_1/2(7+sqrt(48g+1))_|, where |_x_| is the floor function. ...

The Delannoy numbers D(a,b) are the number of lattice paths from (0,0) to (b,a) in which only east (1, 0), north (0, 1), and northeast (1, 1) steps are allowed (i.e., ->, ^, ...

A point lattice is a regularly spaced array of points. In the plane, point lattices can be constructed having unit cells in the shape of a square, rectangle, hexagon, etc. ...

Newton's method, also called the Newton-Raphson method, is a root-finding algorithm that uses the first few terms of the Taylor series of a function f(x) in the vicinity of a ...