Graph theory
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Graph operations
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Binary operation
Graph product
In mathematics, 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 following ta...
Min-plus matrix multiplication
Min-plus matrix multiplication, also known as the distance product, is an operation on matrices.Given two matrices and , their distance product is defined as an matrix such that .This operation is...
Hedetniemi's conjecture
In graph theory, Hedetniemi's conjecture, named after Stephen T. Hedetniemi, concerns the connection between graph coloring and the tensor product of graphs. This conjecture states thatHere χ(G) denot...
Hedetniemi's conjecture - Wikipedia
Cartesian product of graphs
In graph theory, the Cartesian product G H of graphs G and H is a graph such thatCartesian product graphs can be recognized efficiently, in time O(m log n) for a graph with m edges and n vertices (A...
Lexicographic product of graphs
In graph theory, the lexicographic product or graph composition G ∙ H of graphs G and H is a graph such thatIf the edge relations of the two graphs are order relations, then the edge relation of thei...
Lexicographic product of graphs - Wikipedia
Vizing's conjecture
In graph theory, Vizing's conjecture concerns a relation between the domination number and the cartesian product of graphs. This conjecture was first stated by Vadim G. Vizing (1968), and sta...
Vizing's conjecture - Wikipedia
Rooted product of graphs
In mathematical graph theory, the rooted product of a graph G and a rooted graph H is defined as follows: take |V(G)| copies of H, and for every vertex of G, identify with the root node of the i-th ...
Rooted product of graphs - Wikipedia
Zig-zag product
In graph theory, the zig-zag product of regular graphs , denoted by , takes a large graph () and a small graph (), and produces a graph that approximately inherits the size of the large one but the de...
Tensor product of graphs
In graph theory, the tensor product G × H of graphs G and H is a graph such thatThe tensor product is also called the direct product, categorical product, cardinal product, relational product, Krone...
Tensor product of graphs - Wikipedia
Modular product of graphs
In graph theory, the modular product of graphs G and H is a graph such thatCliques in the modular product graph correspond to isomorphisms of induced subgraphs of G and H. Therefore, the modular produ...
Modular product of graphs - Wikipedia
Strong product of graphs
In graph theory, the strong product G ⊠ H of graphs G and H is a graph such thatThe strong product is also called the normal product and AND product. It was first introduced by Sabidussi in 1960.