The king's graph, a strong product of two path graphs
In graph theory, the strong product is a way of combining two graphs to make a larger graph. Two vertices are adjacent in the strong product when they come from pairs of vertices in the factor graphs that are either adjacent or identical. The strong product is one of several different graph product operations that have been studied in graph theory. 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. Decompositions of planar graphs and related graph classes into strong products have been used as a central tool to prove many other results about these graphs.
Care should be exercised when encountering the term strong product in the literature, since it has also been used to denote the tensor product of graphs.[1]
^See page 2 of Lovász, László (1979), "On the Shannon Capacity of a Graph", IEEE Transactions on Information Theory, IT-25 (1): 1–7, doi:10.1109/TIT.1979.1055985.
and 23 Related for: Strong product of graphs information
In graph theory, the strongproduct is a way of combining two graphs to make a larger graph. Two vertices are adjacent in the strongproduct when they...
In graph theory, the tensor 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 vertices...
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...
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...
include the stars, trivially perfect graphs, and friendship graphs. For wheel graphs (the graphsof pyramids), and graphsof higher-dimensional pyramidal polytopes...
of perfect graphs: they are the graphs for which the productof the clique number and independence number is greater than or equal to the number of vertices...
In graph theory, the Shannon capacity of a graph is a graph invariant defined from the number of independent sets ofstronggraphproducts. It is named...
Appendix:Glossary ofgraph theory in Wiktionary, the free dictionary. This is a glossary ofgraph theory. Graph theory is the study ofgraphs, systems of nodes or...
zig-zag productof two expander graphs is also an expander graph, thus zig-zag products can be used inductively to create a family of expander graphs. Intuitively...
particular status. Planar graphs generalize to graphs drawable on a surface of a given genus. In this terminology, planar graphs have genus 0, since the...
signed graphs and gain graphs. Critical graphGraph coloring game Graph homomorphism Hajós construction Mathematics of Sudoku Multipartite graph Uniquely...
preorder on graphs, a distributive lattice, and a category (one for undirected graphs and one for directed graphs). The computational complexity of finding...
1, 0)-adjacency matrix. This matrix is used in studying strongly regular graphs and two-graphs. The distance matrix has in position (i, j) the distance...
undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal...
Cartesian productsof smaller locally linear graphs. Certain Kneser graphs, and certain strongly regular graphs, are also locally linear. The question of how...
Matthew; Chong, Eugene; Banerjee, Jay (2014-03-24). "A Tale of Two Graphs: Property Graphs as RDF in Oracle". {{cite journal}}: Cite journal requires |journal=...
data model of "property graphs" or "attributed graphs " has emerged since the early 2000s as a common denominator of various models ofgraph-oriented databases...
existence of Eulerian circuits is that all vertices in the graph have an even degree, and stated without proof that connected graphs with all vertices of even...
so is their Cartesian product and strongproduct; for instance, the Cartesian productsof two complete graphs, the rook's graphs, are integral. Similarly...
Consumer Research, Pages: 437-441. Gary Chartrand (1977) Graphs as Mathematical Models, chapter 8: Graphs and Social Psychology, Prindle, Webber & Schmidt, ISBN 0-87150-236-4...
Cayley graph is the cycle C n {\displaystyle C_{n}} . More generally, the Cayley graphsof finite cyclic groups are exactly the circulant graphs. The Cayley...
Global Information