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A shortest path between two graph vertices (u,v) of a graph (Skiena 1990, p. 225). There may be more than one different shortest paths, all of the same length. Graph ...

The join G=G_1+G_2 of graphs G_1 and G_2 with disjoint point sets V_1 and V_2 and edge sets X_1 and X_2 is the graph union G_1 union G_2 together with all the edges joining ...

"Vertex" is a synonym for a node of a graph, i.e., one of the points on which the graph is defined and which may be connected by graph edges. The terms "point," "junction," ...

An error which is superimposed on top of a true signal. Noise may be random or systematic. Noise can be greatly reduced by transmitting signals digitally instead of in analog ...

Let G be a simple graph with nonsingular (0,1) adjacency matrix A. If all the diagonal entries of the matrix inverse A^(-1) are zero and all the off-diagonal entries of ...

A word is said to be overlapfree if it has no subwords of the form xyxyx. A squarefree word is overlapfree, and an overlapfree word is cubefree. The numbers t(n) of binary ...

A random graph is a graph in which properties such as the number of graph vertices, graph edges, and connections between them are determined in some random way. The graphs ...

Consider a network of n resistors R_i so that R_2 may be connected in series or parallel with R_1, R_3 may be connected in series or parallel with the network consisting of ...

The square torus is the quotient of the plane by the integer lattice.

The Thomson problem is to determine the stable equilibrium positions of n classical electrons constrained to move on the surface of a sphere and repelling each other by an ...