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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.
It is a commutative operation (for unlabelled graphs); [2] 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 ...
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 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 ...
In graph theory, a rook's graph is an undirected graph that represents all legal moves of the rook chess piece on a chessboard. Each vertex of a rook's graph represents a square on a chessboard, and there is an edge between any two squares sharing a row (rank) or column (file), the squares that a rook can move between. These graphs can be ...
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).