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θ_0 Graph

Image

Alternate name

Basic properties

vertex count | 7
edge count | 8
connected component count | 1

Graph features

Complement graph

Johnson solid skeleton 49

Line graph

(not a named graph)

Graph degrees

vertex degrees | 2 (5 vertices) | 3 (2 vertices)

Topological properties

Graph polynomials

-(x - 1)^2 (x + 1) (x + 2) (x^3 - x^2 - 4 x + 2)

x^6 y^2 + 8 x^6 y + 21 x^6 + 7 x^5 y + 54 x^5 + 2 x^4 y + 70 x^4 + 56 x^3 + 28 x^2 + 8 x + 1

x^6 + 2 x^5 + 3 x^4 + 4 x^3 + 2 x^2 y + 3 x^2 + 3 x y + x + y^2 + y

Coloring properties

chromatic number | 3
edge chromatic number | 3

Spectrum

(-2)^1 (root of 2 - 4 x - x^2 + x^3 near x = -1.81361)^1 (-1)^1 (root of 2 - 4 x - x^2 + x^3 near x = 0.470683)^1 1^2 (root of 2 - 4 x - x^2 + x^3 near x = 2.34292)^1

Associated matrices

(0 | 1 | 0 | 0 | 0 | 1 | 0
1 | 0 | 1 | 0 | 0 | 0 | 0
0 | 1 | 0 | 1 | 0 | 0 | 1
0 | 0 | 1 | 0 | 1 | 0 | 0
0 | 0 | 0 | 1 | 0 | 1 | 0
1 | 0 | 0 | 0 | 1 | 0 | 1
0 | 0 | 1 | 0 | 0 | 1 | 0)

(1 | 1 | 0 | 0 | 0 | 0 | 0 | 0
1 | 0 | 1 | 0 | 0 | 0 | 0 | 0
0 | 0 | 1 | 1 | 1 | 0 | 0 | 0
0 | 0 | 0 | 1 | 0 | 1 | 0 | 0
0 | 0 | 0 | 0 | 0 | 1 | 1 | 0
0 | 1 | 0 | 0 | 0 | 0 | 1 | 1
0 | 0 | 0 | 0 | 1 | 0 | 0 | 1)

Graph indices

Hosoya index | 34
Kirchhoff index | 21.33
stability index | 8
Wiener index | 36

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