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Theory of Computation

Comprehensive encyclopedia of mathematics with 13,000 detailed entries. Continually updated, extensively illustrated, and with interactive examples.

An articulation vertex of a connected graph, also called a cut-vertex (Harary 1994, p. 26; West 2000; Gross and Yellen 2006) or "cutpoint" (Harary 1994, p. 26), is a vertex ...

A simple graph is a line graph of some simple graph iff if does not contain any of the above nine graphs, known in this work as Beineke graphs, as a forbidden induced ...

A block is a maximal connected subgraph of a given graph G that has no articulation vertex (West 2000, p. 155). If a block has more than two vertices, then it is biconnected. ...

delta(x-t)=sum_(n=0)^inftyphi_n(x)phi_n(t), where delta(x) is the delta function.

Coding theory, sometimes called algebraic coding theory, deals with the design of error-correcting codes for the reliable transmission of information across noisy channels. ...

Dijkstra's algorithm is an algorithm for finding a graph geodesic, i.e., the shortest path between two graph vertices in a graph. It functions by constructing a shortest-path ...

The edge chromatic number, sometimes also called the chromatic index, of a graph G is fewest number of colors necessary to color each edge of G such that no two edges ...

An edge cut (Holton and Sheehan 1993, p. 14; West 2000, p. 152), edge cut set, edge cutset (Holton and Sheehan 1993, p. 14), or sometimes simply "cut set" or "cutset" (e.g., ...