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The strong product of any two graphs can be constructed as the union of two other products of the same two graphs, the Cartesian product of graphs and the tensor product of graphs. An example of a strong product is the king's graph, the graph of moves of a chess king on a chessboard, which can be constructed as a strong product of path graphs ...
Pages in category "Graph products" The following 12 pages are in this category, out of 12 total. ... Strong product of graphs; T. Tensor product of graphs; V. Vizing ...
In graph theory, a graph product is a binary operation on graphs. Specifically, it is an operation that takes two graphs G 1 and G 2 and produces a graph H with the following properties: The vertex set of H is the Cartesian product V ( G 1 ) × V ( G 2 ) , where V ( G 1 ) and V ( G 2 ) are the vertex sets of G 1 and G 2 , respectively.
In graph theory, the replacement product of two graphs is a graph product that can be used to reduce the degree of a graph while maintaining its connectivity. [1] Suppose G is a d-regular graph and H is an e-regular graph with vertex set {0, …, d – 1}. Let R denote the replacement product of G and H. The vertex set of R is the Cartesian ...
In graph theory, the Shannon capacity of a graph is a graph invariant defined from the number of independent sets of strong graph products. It is named after American mathematician Claude Shannon . It measures the Shannon capacity of a communications channel defined from the graph, and is upper bounded by the Lovász number , which can be ...
If a connected graph is a Cartesian product, it can be factorized uniquely as a product of prime factors, graphs that cannot themselves be decomposed as products of graphs. [2] However, Imrich & Klavžar (2000) describe a disconnected graph that can be expressed in two different ways as a Cartesian product of prime graphs:
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Powers of graphs are referred to using terminology similar to that of exponentiation of numbers: G 2 is called the square of G, G 3 is called the cube of G, etc. [1] Graph powers should be distinguished from the products of a graph with itself, which (unlike powers) generally have many more vertices than the original graph.