Search Results for ""

A walk is a sequence v_0, e_1, v_1, ..., v_k of graph vertices v_i and graph edges e_i such that for 1<=i<=k, the edge e_i has endpoints v_(i-1) and v_i (West 2000, p. 20). ...

A weighted adjacency matrix A_f of a simple graph is defined for a real positive symmetric function f(d_i,d_j) on the vertex degrees d_i of a graph as ...

A white 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), when ...

WireWorld is a two-dimensional four-color cellular automaton introduced by Brian Silverman in 1987. The rule for the automaton uses the cell's old value a together with the ...

x^n=sum_(k=0)^n<n; k>(x+k; n), where <n; k> is an Eulerian number and (n; k) is a binomial coefficient (Worpitzky 1883; Comtet 1974, p. 242).

Young's geometry is a finite geometry which satisfies the following five axioms: 1. There exists at least one line. 2. Every line of the geometry has exactly three points on ...

The first and second Zagreb indices for a graph with vertex count n and vertex degrees v_i for i=1, ..., n are defined by Z_1=sum_(i=1)^nv_i^2 and Z_2=sum_((i,j) in ...

A zero-symmetric graph is a vertex-transitive cubic graph whose edges are partitioned into three orbits by its automorphism group. The figures above show some small ...

A k-coloring of a graph G is a vertex coloring that is an assignment of one of k possible colors to each vertex of G (i.e., a vertex coloring) such that no two adjacent ...

Graphs corresponding to closed walks of length k are known as k-cyclic graphs, or C_k-graphs for short. C_k-graphs are connected by definition. The numbers of C_k-graphs for ...