Search results
Results From The WOW.Com Content Network
This two-graph is a regular two-graph since each pair of distinct vertices appears together in exactly two triples. Given a simple graph G = (V,E), the set of triples of the vertex set V whose induced subgraph has an odd number of edges forms a two-graph on the set V. Every two-graph can be represented in this way. [1]
A Cartesian product of two 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,v) and (u' ,v' ) are adjacent in G H if and only if either u = u' and v is adjacent to v' in H, or; v = v' and u is adjacent to u' in G.
In graph theory, a graph product is a binary operation on graphs. Specifically, it is an operation that takes two graphs G 1 and G 2 and produces a graph H with the following properties: 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.
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
A connected graph G is planar if and only if it has an algebraic dual. The same fact can be expressed in the theory of matroids. If M is the graphic matroid of a graph G, then a graph G * is an algebraic dual of G if and only if the graphic matroid of G * is the dual matroid of M.
In general, a subdivision of a graph G (sometimes known as an expansion [2]) is a graph resulting from the subdivision of edges in G. The subdivision of some edge e with endpoints {u,v } yields a graph containing one new vertex w, and with an edge set replacing e by two new edges, {u,w } and {w,v }. For directed edges, this operation shall ...
Two graphs are homomorphically equivalent if there exist two homomorphisms, one from each graph to the other graph. homomorphism 1. A graph homomorphism is a mapping from the vertex set of one graph to the vertex set of another graph that maps adjacent vertices to adjacent vertices. This type of mapping between graphs is the one that is most ...
A set of graphs isomorphic to each other is called an isomorphism class of graphs. The question of whether graph isomorphism can be determined in polynomial time is a major unsolved problem in computer science, known as the graph isomorphism problem. [1] [2] The two graphs shown below are isomorphic, despite their different looking drawings.