Planar graph - Wikipedia
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other.
What is a Planar Graph?: Definition, Properties, & Applications
Sep 8, 2023 · In graph theory, a Planar Graph is a type of graph that can be drawn on a flat surface (such as a piece of paper) without any of its edges crossing each other.
These notes cover special properties of planar graphs. planar graph is a graph which can be drawn in the plane without any edges crossing. Some pictures of a planar graph might have crossing edges, but it’s possible to redraw the picture to eliminate the crossings.
Planar Graphs - openmathbooks.github.io
When a connected graph can be drawn without any edges crossing, it is called planar. When a planar graph is drawn in this way, it divides the plane into regions called faces. Draw, if possible, two different planar graphs with the same number of vertices, edges, and faces.
Planar Embedding -- from Wolfram MathWorld
Jan 14, 2025 · A planar embedding, also called a "plane graph" (Harary 1994, p. 103; Harborth and Möller 1994), "planar drawing," or "plane drawing," of a planar graph is an embedding in which no two edges intersect (or overlap) and no two vertices coincide.
A graph is called planar if it can be drawn in the plane (R2) with vertex v drawn as a point f(v) 2R 2 , and edge (u;v) drawn as a continuous curve between f(u) and f(v), such that no two edges intersect (except possibly at the end-points).
5.3 Planar Graphs and Euler’s Formula Among the most ubiquitous graphs that arise in applications are those that can be drawn in the plane without edges crossing.
Oct 22, 2024 · A planar graph is still just an abstract object: a set of vertices and a set of edges. We haven’t picked a particular drawing for it, and there could be many drawings that are different from each other in important ways. We say that a plane embedding of a graph G is a drawing of G in the plane with no crossings.
Definition 5.1.1: We say that G is planar if it can be drawn on the plane such that its edges intersect only at their end vertices. Such a drawing is called a planar embedding or plane drawing. A plane graph of G is a fixed embedding of G on the plane and a graph that is …
Plane Graph: A plane graph is a graph drawn in the plane so that every vertex is a distinct point, and every edge with ends u; v is represented by a curve with endpoints corresponding to u; v so that none of these curves intersect one another except at the endpoints.