Petersen graph

Petersen graph

Named after	Julius Peter Christian Petersen
size	10 knots, 15 edges
properties	snark , cubic .
Chromatic number	3
Chromatic index	4th
Nodal context	3
Clique count	2
Number of cuts	2
Chromatic polynomial	${\displaystyle t(t-1)(t-2)(t^{7}-12t^{6}+67t^{5}-}$ ${\displaystyle 230t^{4}+529t^{3}-814t^{2}+775t-352)}$
Characteristic polynomial	${\displaystyle (t-1)^{5}(t+2)^{4}(t-3)}$
LCF notation

The Petersen graph (named after the Danish mathematician Julius Petersen ) is a 3- regular (i.e. cubic) graph with 10 nodes . This means that each of the nodes has three neighbors, so the degree sequence is (3,3,3,3,3,3,3,3,3,3). The Petersen graph is an example and counterexample that is often used in graph theory . It also occurs in tropical geometry .

Properties of the Petersen graph:

• Cubic or 3- regular (by definition )
• Not planar
• Coherently
• Symmetrical
• The length of the shortest circle is 5
• Does not contain a Hamilton cycle
• Smallest hypohamiltonian graph
• Chromatic number (graph theory) 3
• Chromatic index (graph theory) 4
• Is not a Cayley graph , although it is regular and locally finite.

The Petersen graph belongs to a group of connected, unbroken, and non-planar graphs known as " snark ".

See also: Types of graphs in graph theory in Graph (graph theory)

Web links

• Eric W. Weisstein : Petersen graph . In: MathWorld (English).

Commons : Petersen Graph  - collection of images, videos and audio files