In the mathematical discipline of graph theory, the dual graph of a planar graph G is a graph that has a vertex for each face of G. The dual graph has an edge for each pair of faces in G that …

Apr 30, 2025 · The dual graph of a polyhedral graph has graph vertices each of which corresponds to a face of and each of whose faces corresponds to a graph vertex of . Two …

Mar 12, 2023 · Two vertices f∗ and g are joined by the edge e∗ in G∗ if and only if their corresponding faces f and g are separated by edge e in G. Graph G ∗ is the dual of G.

Jan 16, 2012 · The dual graph consist of three vertices 1, 2 and 3 such that there are three edges between 1 and 2, three edges between 2 and 3, one loop at the vertex 2.

Apr 14, 2021 · In West's Introduction To Graph Theory, he gives the following definition of the graph dual: Definition 6.1.7: The dual graph $G^*$ of a plane graph $G$ is a plane graph …

Dual graphs have been used to prove a variety of theorems in graph theory, including the famous four-color theorem, which states that any planar map can be colored using no more than four …

In the mathematical discipline of graph theory, the dual graph of a plane graph G is a graph that has a vertex corresponding to each face of G, and an edge joining two neighboring faces for …

In this section we discuss two important concepts in graph theory – planarity and duality. First we consider planar graphs and derived some properties of these graphs then the dual graphs and …

Given a graph G,itsline graph or derivative L[G] is a graph such that (i) each vertex of L[G] represents an edge of G and (ii) two vertices of L[G] are adjacent if and only if their …

Definition: For a planar graph G, the dual of G denoted G∗ is a graph obtained by replacing all faces in G with vertices, and connecting vertices with edges if those faces share an edge. For …