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Petersen Graph

Image

Notation

GP(5, 2)

Alternate names

Basic properties

vertex count | 10
edge count | 15
connected component count | 1

Graph features

Complement graph

5-triangular graph

Line graph

Petersen line graph

Graph degrees

vertex degrees | 3 (10 vertices)

Topological properties

Graph polynomials

(x - 3) (x - 1)^5 (x + 2)^4

x^9 y^6 + 15 x^9 y^5 + 105 x^9 y^4 + 445 x^9 y^3 + 1230 x^9 y^2 + 2172 x^9 y + 2000 x^9 + 10 x^8 y^4 + 135 x^8 y^3 + 816 x^8 y^2 + 2765 x^8 y + ... + 30 x^6 y^2 + 630 x^6 y + 4875 x^6 + 130 x^5 y + 2991 x^5 + 12 x^4 y + 1365 x^4 + 455 x^3 + 105 x^2 + 15 x + 1 (27 terms)

x^9 + 6 x^8 + 21 x^7 + 56 x^6 + 12 x^5 y + 114 x^5 + 70 x^4 y + 170 x^4 + 30 x^3 y^2 + 170 x^3 y + 180 x^3 + 15 x^2 y^3 + 105 x^2 y^2 + 240 x^2 y + 120 x^2 + 10 x y^4 + 65 x y^3 + 171 x y^2 + 168 x y + 36 x + y^6 + 9 y^5 + 35 y^4 + 75 y^3 + 84 y^2 + 36 y

Coloring properties

chromatic number | 3
edge chromatic number | 4

Spectrum

(-2)^4 1^5 3^1

Associated matrices

Associated matrices Adjacency matrix

Associated matrices Incidence matrix

Graph indices

Hosoya index | 332
Kirchhoff index | 33
stability index | 424
Wiener index | 75

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