Search results
Results from the WOW.Com Content Network
The standard playing card ranks {A, K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, 2} form a 13-element set. The card suits {♠, ♥, ♦, ♣} form a four-element set. The Cartesian product of these sets returns a 52-element set consisting of 52 ordered pairs, which correspond to all 52 possible playing cards.
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 K 2 C n. The rook's graph is the Cartesian product of two complete graphs.
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. Two vertices (a 1,a 2) and (b 1,b 2) of H are connected by an edge, iff a condition about a 1, b 1 in G 1 and a 2, b 2 in G 2 is fulfilled. The graph products differ in what exactly this condition is.
3 Two sets involved. ... 7.2.3.1 Incorrectly distributing by swapping ⋂ and ... and binary Cartesian product , and it is also a ...
In set theory, a Cartesian product is a mathematical operation which returns a set (or product set) from multiple sets. That is, for sets A and B, the Cartesian product A × B is the set of all ordered pairs (a, b) —where a ∈ A and b ∈ B. [5] The class of all things (of a given type) that have Cartesian products is called a Cartesian ...
The axiom of choice occurs again in the study of (topological) product spaces; for example, Tychonoff's theorem on compact sets is a more complex and subtle example of a statement that requires the axiom of choice and is equivalent to it in its most general formulation, [3] and shows why the product topology may be considered the more useful ...
2. In geometry and linear algebra, denotes the cross product. 3. In set theory and category theory, denotes the Cartesian product and the direct product. See also × in § Set theory. · 1. Denotes multiplication and is read as times; for example, 3 ⋅ 2. 2. In geometry and linear algebra, denotes the dot product. 3.
For instance, for a star K 1,n, its domination number γ(K 1,n) is one: it is possible to dominate the entire star with a single vertex at its hub. Therefore, for the graph G = K 1,n K 1,n formed as the product of two stars, Vizing's conjecture states only that the domination number should be at least 1 × 1 = 1. However, the domination number ...