# 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:

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)