In graph theory, a graph product is a binary operation on graphs. Specifically, it is an operation that takes two graphs G1 and G2 and produces a graph H with the following properties: The vertex set of H is the Cartesian product V(G1) × V(G2), where V(G1) and V(G2) are the vertex sets of G1 and G2, respectively.

The cartesian product of graphs is one of two graph products that turn the category of graphs and graph homomorphisms into a symmetric closed monoidal category (as opposed to merely symmetric monoidal), the other being the tensor product of graphs. [8]

The Cartesian graph product G=G_1 square G_2, also called the graph box product and sometimes simply known as "the" graph product (Beineke and Wilson 2004, p. 104) and sometimes denoted G_1×G_2 (e.g., Salazar and Ugalde 2004; though this notation is more commonly used for the distinct graph tensor product) of graphs G_1 and G_2 with disjoint ...

6 天之前 · In general, a graph product of two graphs G and H is a new graph whose vertex set is V(G)×V(H) and where, for any two vertices (g,h) and (g^',h^') in the product, the adjacency of those two vertices is determined entirely by the adjacency (or equality, or non-adjacency) of g and g^', and that of h and h^'.

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' h is adjacent to h'.

Products of graphs# This module gathers everything related to graph products. At the moment it contains an implementation of a recognition algorithm for graphs that can be written as a Cartesian product of smaller ones.

Explore the various graph products in graph theory, including Cartesian product, tensor product, and more. Understand their properties and applications.

Graph product is a very basic idea in graph theory. Graph products include a wide range of operations that join two or more existing graphs to produce new graphs with distinctive properties and uses. In this paper, we explore four forms of graph products, their characteristics, and their significance within the broader framework of graph theory.

2020年1月24日 · In particular, we characterise when a graph class defined by a cartesian or strong product has bounded or polynomial expansion. We then explore graph product structure theorems for various geometrically defined graph classes, and present several open problems.

D: Products and Cayley Graphs D1 Product Graphs There are multiple ways to combine two graphs to get a new one. For a prod-uct of graphs Gand H, the vertex set is the set of ordered pairs (g,h) where g∈V(G) and h∈V(H). The most common product is the cartesian product written G H. Here two pairs are adjacent if they are the same in one coor-