In graph theory, the tensor productG × 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 tensor product is also called the direct product, Kronecker product, categorical product, cardinal product, relational product, weak direct product, or conjunction. As an operation on binary relations, the tensor product was introduced by Alfred North Whitehead and Bertrand Russell in their Principia Mathematica (1912). It is also equivalent to the Kronecker product of the adjacency matrices of the graphs.[1]
The notation G × H is also (and formerly normally was) used to represent another construction known as the Cartesian product of graphs, but nowadays more commonly refers to the tensor product. The cross symbol shows visually the two edges resulting from the tensor product of two edges.[2] This product should not be confused with the strong product of graphs.
^Weichsel 1962.
^Hahn & Sabidussi 1997.
and 24 Related for: Tensor product of graphs information
In graph theory, the tensorproduct G × H ofgraphs G and H is a graph such that the vertex set of G × H is the Cartesian product V(G) × V(H); and vertices...
v\otimes w} is called the tensorproductof v and w. An element of V ⊗ W {\displaystyle V\otimes W} is a tensor, and the tensorproductof two vectors is sometimes...
In graph theory, the Cartesian product G □ H ofgraphs G and H is a graph such that: the vertex set of G □ H is the Cartesian product V(G) × V(H); and...
Cartesian productofgraphs is not a product in the sense of category theory. Instead, the categorical product is known as the tensorproductofgraphs. Axiom...
graph theory, a graphproduct is a binary operation on graphs. Specifically, it is an operation that takes two graphs G1 and G2 and produces a graph H...
In multilinear algebra, a tensor decomposition is any scheme for expressing a "data tensor" (M-way array) as a sequence of elementary operations acting...
descriptions of redirect targets Tensor product of graphs – Operation in graph theory Orders on the Cartesian productof totally ordered sets – Order whose elements...
product, sometimes denoted by ⊗, is an operation on two matrices of arbitrary size resulting in a block matrix. It is a specialization of the tensor product...
and one loop at that vertex. The tensorproductofgraphs is the category-theoretic product and the exponential graph is the exponential object for this...
generally, in this case, the tensorproductofgraphs between any m- and n-vertex circulants is itself a circulant. Many of the known lower bounds on Ramsey...
cover of G is the tensorproductofgraphs G × K2: If G is already bipartite, its bipartite double cover consists of two disjoint copies of G. A graph may...
as the tensorproductofgraphs, G × K2. It is also called the Kronecker double cover, canonical double cover or simply the bipartite double of G. It should...
Tensor networks or tensor network states are a class of variational wave functions used in the study of many-body quantum systems. Tensor networks extend...
graph product: it is a commutative and associative operation (for unlabelled graphs), tensorgraphproduct (or direct graphproduct, categorical graph product...
between the Ricci tensor and the matter content of the universe. Like the metric tensor, the Ricci tensor assigns to each tangent space of the manifold a...
Cross product Dot product representation of a graph Euclidean norm, the square-root of the self dot product Matrix multiplication Metric tensor Multiplication...
theory, and various areas of analytic philosophy. He was one of the early 20th century's prominent logicians and a founder of analytic philosophy, along...
representation of a knowledge graph's entities and relations while preserving their semantic meaning. Leveraging their embedded representation, knowledge graphs (KGs)...
other sets of generators as well. The Cayley graphsof cyclic groups with arbitrary generator sets are called circulant graphs. These graphs may be represented...
smartphone series in 2021, and were succeeded by the Tensor G2 chip in 2022 and G3 in 2023. Tensor has been generally well received by critics. Development...
space is the time derivative of the angular displacement tensor, which is a second rank skew-symmetric tensor. This tensor Ω will have n(n−1)/2 independent...
complete graph, as the tensorproduct Kn × K2, as the complement of the Cartesian direct productof Kn and K2, or as a bipartite Kneser graph Hn,1 representing...
Global Information