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A pair of vertices (x,y) of a graph G is called an omega-critical pair if omega(G+xy)>omega(G), where G+xy denotes the graph obtained by adding the edge xy to G and omega(H) ...

The Byzantine generals problem considers a computer with many programs running, some of them possibly unfriendly, and asks how the computer can function properly. More ...

Two nonisomorphic graphs are said to be chromatically equivalent (also termed "chromically equivalent by Bari 1974) if they have identical chromatic polynomials. A graph that ...

A circular embedding is a graph embedding in which all graph vertices lie on a common circle, usually arranged so they are equally spaced around the circumference. Specific ...

A function H that maps an arbitrary length message M to a fixed length message digest MD is a collision-free hash function if 1. It is a one-way hash function. 2. It is hard ...

Let m(G) be the cycle rank of a graph G, m^*(G) be the cocycle rank, and the relative complement G-H of a subgraph H of G be defined as that subgraph obtained by deleting the ...

The n-cycle complement graph C^__n is the graph complement of the cycle graph C_n. Cycle complement graphs are special cases of circulant graphs. The first few are ...

The discrete Fourier transform of length N (where N is even) can be rewritten as the sum of two discrete Fourier transforms, each of length N/2. One is formed from the ...

A (Delta,D)-graph is a graph with maximum vertex degree Delta and diameter at most D. The order of a graph with degree Delta of diameter D is bounded by ...

A search algorithm of a tree that explores the first child of a node before visiting its siblings. Tarjan (1972) and Hopcroft and Tarjan (1973) showed that depth-first search ...