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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, 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, 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.
The yellow directed acyclic graph is the condensation of the blue directed graph. It is formed by contracting each strongly connected component of the blue graph into a single yellow vertex. If each strongly connected component is contracted to a single vertex, the resulting graph is a directed acyclic graph, the condensation of G.
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 ...
In graph theory, the strength of an undirected graph corresponds to the minimum ratio of edges removed/components created in a decomposition of the graph in question. It is a method to compute partitions of the set of vertices and detect zones of high concentration of edges, and is analogous to graph toughness which is defined similarly for vertex removal.
The tensor product of graphs. In graph theory, the tensor product G × H of graphs G and H is a graph such that the vertex set of G × H is the Cartesian product V(G) × V(H); and; vertices (g,h) and (g',h' ) are adjacent in G × H if and only if. g is adjacent to g' in G, and; h is adjacent to h' in H.