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GraphTheory

  

IsIntegerGraph

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

IsIntegerGraph(G)

Parameters

G

-

a graph

Description

• 

IsIntegerGraph returns true if its argument G is an integer graph, namely if the spectrum of G consists of only integer numbers, and false otherwise.

Examples

withGraphTheory:

withSpecialGraphs:

K3CompleteGraph3

K3Graph 1: an undirected unweighted graph with 3 vertices and 3 edge(s)

(1)

IsIntegerGraphK3

true

(2)

factorCharacteristicPolynomialK3,x

x2x+12

(3)

P3PathGraph3

P3Graph 2: an undirected unweighted graph with 3 vertices and 2 edge(s)

(4)

IsIntegerGraphP3

false

(5)

factorCharacteristicPolynomialP3,x

xx22

(6)

HLeviGraph

HGraph 3: an undirected unweighted graph with 30 vertices and 45 edge(s)

(7)

IsIntegerGraphH

true

(8)

factorCharacteristicPolynomialH,x

x10x3x+3x29x+29

(9)

See Also

CharacteristicPolynomial

GraphSpectrum