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The Cartesian product of two path graphs is a grid graph. The Cartesian product of n edges is a hypercube: =. Thus, the Cartesian product of two hypercube graphs is another hypercube: Q i Q j = Q i+j. The Cartesian product of two median graphs is another median graph. The graph of vertices and edges of an n-prism is the Cartesian product graph ...
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.
tensor graph product (or direct graph product, categorical graph product, cardinal graph product, Kronecker graph product): it is a commutative and associative operation (for unlabelled graphs), zig-zag graph product; [3] graph product based on other products: rooted graph product: it is an associative operation (for unlabelled but rooted ...
The circular ladder graph CL n is constructible by connecting the four 2-degree vertices in a straight way, or by the Cartesian product of a cycle of length n ≥ 3 and an edge. [4] In symbols, CL n = C n × P 2. It has 2n nodes and 3n edges. Like the ladder graph, it is connected, planar and Hamiltonian, but it is bipartite if and only if n is ...
Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.
An optimal five-vertex dominating set in the product of two stars, K 1,4 K 1,4. Examples such as this one show that, for some graph products, Vizing's conjecture can be far from tight. A 4-cycle C 4 has domination number two: any single vertex only dominates itself and its two neighbors, but any pair of vertices dominates the whole graph.
In the category of groups, the product is the direct product of groups given by the Cartesian product with multiplication defined componentwise. In the category of graphs, the product is the tensor product of graphs. In the category of relations, the product is given by the disjoint union.