Search Results for ""

The perpendicular foot, also called the foot of an altitude, is the point on the leg opposite a given vertex of a triangle at which the perpendicular passing through that ...

Let the center B of a circle of radius a move along a line BA. Let O be a fixed point located a distance c away from AB. Draw a secant line through O and D, the midpoint of ...

The chromatic polynomial pi_G(z) of an undirected graph G, also denoted C(G;z) (Biggs 1973, p. 106) and P(G,x) (Godsil and Royle 2001, p. 358), is a polynomial which encodes ...

A bishop graph is a graph formed from possible moves of a bishop chess piece, which may make diagonal moves of any length on a chessboard (or any other board). To form the ...

Every nonplanar graph contains either the utility graph K_(3,3) (i.e., the complete bipartite graph on two sets of three vertices) or the pentatope graph K_5 as a ...

The ABC (atom-bond connectivity) energy of a graph is defined as the graph energy of its ABC matrix, i.e., the sum of the absolute values of the eigenvalues of its ABC matrix.

The Pappus configuration is the 9_3 configuration illustrated above that appears in Pappus's hexagon theorem. It is one of the three 9_3 configurations. The Levi graph of the ...

The Cartesian product of two sets A and B (also called the product set, set direct product, or cross product) is defined to be the set of all points (a,b) where a in A and b ...

Let DeltaH_AH_BH_C be the orthic triangle of a triangle DeltaABC. Then each side of each triangle meets the three sides of the other triangle, and the points of intersection ...

An acyclic digraph is a directed graph containing no directed cycles, also known as a directed acyclic graph or a "DAG." Every finite acyclic digraph has at least one node of ...