Dipole graph
Encyclopedia
In graph theory
, a dipole graph (or dipole) is a multigraph
consisting of two vertices
connected with a number of edges. A dipole graph containing n edges is called the order-n dipole graph, and is denoted by Dn. The order-n dipole graph is dual
to the cycle graph
Cn.
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
, a dipole graph (or dipole) is a multigraph
Multigraph
In mathematics, a multigraph or pseudograph is a graph which is permitted to have multiple edges, , that is, edges that have the same end nodes. Thus two vertices may be connected by more than one edge....
consisting of two vertices
Vertex (graph theory)
In graph theory, a vertex or node is the fundamental unit out of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges , while a directed graph consists of a set of vertices and a set of arcs...
connected with a number of edges. A dipole graph containing n edges is called the order-n dipole graph, and is denoted by Dn. The order-n dipole graph is dual
Dual graph
In mathematics, the dual graph of a given planar graph G is a graph which has a vertex for each plane region of G, and an edge for each edge in G joining two neighboring regions, for a certain embedding of G. The term "dual" is used because this property is symmetric, meaning that if H is a dual...
to the cycle graph
Cycle graph
In graph theory, a cycle graph or circular graph is a graph that consists of a single cycle, or in other words, some number of vertices connected in a closed chain. The cycle graph with n vertices is called Cn...
Cn.