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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.
graph products based on the cartesian product of the vertex sets: 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 ]
The Hamming graph H(d,q) has vertex set S d, the set of ordered d-tuples of elements of S, or sequences of length d from S. Two vertices are adjacent if they differ in precisely one coordinate; that is, if their Hamming distance is one. The Hamming graph H(d,q) is, equivalently, the Cartesian product of d complete graphs K q. [1]
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 ...
The lexicographic product of graphs. In graph theory, the lexicographic product or (graph) composition 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; any two vertices (u,v) and (x,y) are adjacent in G ∙ H if and only if either u is adjacent to x in G or u = x and v is ...
Cartesian product of graphs; H. Hedetniemi's conjecture; L. Lexicographic product of graphs; M. Min-plus matrix multiplication; Modular product of graphs; R ...