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A Cartesian product of two graphs. In graph theory, the Cartesian 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; two vertices (u,v) and (u' ,v' ) are adjacent in G H if and only if either u = u' and v is adjacent to v' in H, or; v = v' and u is adjacent to u' in G.
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 Cartesian product of two graphs G and H is the graph denoted by G × H, whose vertex set is the (ordinary) Cartesian product V(G) × V(H) and such that two vertices (u,v) and (u′,v′) are adjacent in G × H, if and only if u = u′ and v is adjacent with v ′ in H, or v = v′ and u is adjacent with u ′ in G.
cartesian graph product: it is a commutative and associative operation (for unlabelled graphs), [2] lexicographic graph product (or graph composition): it is an associative (for unlabelled graphs) and non-commutative operation, [2] strong graph product: it is a commutative and associative operation (for unlabelled graphs), tensor graph product ...
Economic graphs are presented only in the first quadrant of the Cartesian plane when the variables conceptually can only take on non-negative values (such as the quantity of a product that is produced). Even though the axes refer to numerical variables, specific values are often not introduced if a conceptual point is being made that would ...
In the mathematical field of graph theory, the ladder graph L n is a planar, undirected graph with 2n vertices and 3n – 2 edges. [1] The ladder graph can be obtained as the Cartesian product of two path graphs, one of which has only one edge: L n,1 = P n × P 2. [2] [3]
The Bills beat the Broncos in the wild card round of the 2025 NFL playoffs. Here's a look at who the Bills will play next.
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 ...