What is the genus of planar graph?

Planar graphs generalize to graphs drawable on a surface of a given genus. In this terminology, planar graphs have genus 0, since the plane (and the sphere) are surfaces of genus 0.

Is K6 a planar graph?

Thus K6 and K4,5 are nonplanar. In fact, any graph which contains a “topological embedding” of a nonplanar graph is non- planar. A topological embedding of a graph H in a graph G is a subgraph of G which is isomorphic to a graph obtained by replacing each edge of H with a path (with the paths all vertex disjoint).

What is genus graph theory?

Graph theory The genus of a graph is the minimal integer n such that the graph can be drawn without crossing itself on a sphere with n handles (i.e. an oriented surface of genus n). Thus, a planar graph has genus 0, because it can be drawn on a sphere without self-crossing.

How do you find the crossing number of a graph?

In graph theory, the crossing number cr(G) of a graph G is the lowest number of edge crossings of a plane drawing of the graph G. For instance, a graph is planar if and only if its crossing number is zero.

How do you draw a planar graph?

When a planar graph is drawn in this way, it divides the plane into regions called faces .

  1. Draw, if possible, two different planar graphs with the same number of vertices, edges, and faces.
  2. Draw, if possible, two different planar graphs with the same number of vertices and edges, but a different number of faces.

How do you know if a graph is planar?

Planar Graphs: A graph G= (V, E) is said to be planar if it can be drawn in the plane so that no two edges of G intersect at a point other than a vertex. Such a drawing of a planar graph is called a planar embedding of the graph.

Is K7 graph planar?

By Kuratowski’s theorem, K7 is not planar. Thus, K7 is toroidal.

Is K8 planar graph?

K7 is a toroidal graph (it is embeddable on the torus), K8 is not.

What are the different types of genus?

Numbers of accepted genera

  • Animalia: 239,093 accepted genus names (± 55,350)
  • Plantae: 28,724 accepted genus names (± 7,721)
  • Fungi: 10,468 accepted genus names (± 182)
  • Chromista: 11,114 accepted genus names (± 1,268)
  • Protozoa: 3,109 accepted genus names (± 1,206)
  • Bacteria: 3,433 accepted genus names (± 115)

What is an example of a genus?

genus: (plural: genera) A group of closely related species. For example, the genus Canis — which is Latin for “dog” — includes all domestic breeds of dog and their closest wild relatives, including wolves, coyotes, jackals and dingoes. Homo: A genus of species that includes modern humans (Homo sapiens).

Is K5 3 a planar graph?

The graph K5 is non-planar. Proof: in K5 we have v = 5 and e = 10, hence 3v − 6 = 9 < e = 10, which contradicts the previous result. 4. The graph K3,3 is non-planar.