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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 ...
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.
Strong product of graphs; T. Tensor product of graphs; V. Vizing's conjecture; Z. Zig-zag product This page was last edited on 18 December 2020, at 00:02 (UTC) ...
strong graph product: it is a commutative and associative operation (for unlabelled graphs), 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 ...
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.
The strong product of any two graphs of bounded twin-width, one of which has bounded degree, again has bounded twin-width. This can be used to prove the bounded twin-width of classes of graphs that have decompositions into strong products of paths and bounded-treewidth graphs, such as the k-planar graphs. [3]
Each vertex in the strong product corresponds to a pair of vertices in each of two factor graphs. The cop can win in a strong product of two cop-win graphs by, first, playing to win in one of these two factor graphs, reaching a pair whose first component is the same as the robber. Then, while staying in pairs whose first component is the same ...
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 ...