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CharacteristicPolynomial

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

CharacteristicPolynomial(G, x)

Parameters

G

-

undirected graph

x

-

variable or value

Description

• 

CharacteristicPolynomial returns the characteristic polynomial of the adjacency matrix of a graph G, as a polynomial in x.

Examples

withGraphTheory:

withSpecialGraphs:

PGraph1,2,2,3

P:=Graph 1: an undirected unweighted graph with 3 vertices and 2 edge(s)

(1)

CharacteristicPolynomialP,x

x32x

(2)

AAdjacencyMatrixP

A:=010101010

(3)

LinearAlgebra[CharacteristicPolynomial]A,x

x32x

(4)

GShrikhandeGraph:

DiameterG

2

(5)

fCharacteristicPolynomialG,x

f:=x1648x1464x13+768x12+1536x115888x1015360x9+23040x8+81920x736864x6245760x532768x4+393216x3+196608x2262144x196608

(6)

eigvalssolvef

eigvals:=2,2,6

(7)

numelemseigvals

3

(8)

See Also

AdjacencyMatrix

GraphSpectrum

LinearAlgebra[CharacteristicPolynomial]

 


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