# Category: Graph products

Strong product of 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
Min-plus matrix multiplication
Min-plus matrix multiplication, also known as distance product, is an operation on matrices. Given two matrices and , their distance product is defined as an matrix such that . This is standard matrix
Tensor product of graphs
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 ×
Replacement product
In graph theory, the replacement product of two graphs is a graph product that can be used to reduce the degree of a graph while maintaining its connectivity. Suppose G is a d-regular graph and H is a
Igraph
igraph is a library collection for creating and manipulating graphs and analyzing networks. It is written in C and also exists as Python and R packages. There exists moreover an interface for Mathemat
Lexicographic product of graphs
In graph theory, the lexicographic product or (graph) composition 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 * any two vertices
Tellagraf
ISSCO's Tellagraf is an early software package designed to allow end-users to "turn out full color, professional quality charts" with initial results displayed on a screen, modified as needed, and the
Zig-zag product
In graph theory, the zig-zag product of regular graphs , denoted by , is a binary operation which takes a large graph and a small graph and produces a graph that approximately inherits the size of the
Hedetniemi's conjecture
In graph theory, Hedetniemi's conjecture, formulated by in 1966, concerns the connection between graph coloring and the tensor product of graphs. This conjecture states that Here denotes the chromatic
Graph product
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 s
Modular product of graphs
In graph theory, the modular product of graphs G and H is a graph formed by combining G and H that has applications to subgraph isomorphism.It is one of several different kinds of graph products that
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, and states that, if γ(G
Cartesian product of graphs
In graph theory, the Cartesian 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 * two vertices (u,u' ) and (v,v' ) are adjace
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 co