Get Math Help

Star Graph

Image

Alternate name

Basic properties

vertex count | 45
edge count | 85
connected component count | 1

Graph features

Complement graph

(not a named graph)

Line graph

(not a named graph)

Graph degrees

vertex degrees | 3 (35 vertices) | 6 (5 vertices) | 7 (5 vertices)

Topological properties

Graph polynomials

-(x^3 + x^2 - 2 x - 1) (x^6 - 5 x^5 - 4 x^4 + 35 x^3 - 26 x^2 - 10 x + 8) (x^18 + 2 x^17 - 31 x^16 - 52 x^15 + 400 x^14 + ... + 9232 x^2 - 119 x - 1 (19 terms))^2

Coloring properties

chromatic number | 4
edge chromatic number | 7

Spectrum

(-3.32026)^2 (-3.16465)^2 (-2.64639)^1 (-2.23882)^2 (-1.89138)^2 (-1.80194)^1 (-1.75836)^2 (-1.64422)^2 (-1.10058)^2 (-1.0893)^2 (-0.544502)^1 (-0.445042)^1 (-0.005793)^2 0.0188314^2 0.538712^1 1.00424^2 1.10107^1 1.16886^2 1.24698^1 1.26108^2 1.30168^2 2.10531^1 2.14267^2 2.22022^2 2.46332^2 2.63248^2 4.44581^1

Associated matrices

Associated matrices Adjacency matrix

Associated matrices Incidence matrix

Graph indices

Hosoya index | 1.626 trillion
Kirchhoff index | 813.7
stability index | 2.418 trillion
Wiener index | 2670

Why Club Z!?

We're Awesome!

Vestibulum vitae aliquam nunc. Suspendisse mollis metus ac tellus egestas pharetra. Suspendisse at viverra purus. Pellentesque nec posuere ligula, eu congue leo. Integer vulputate tempor arcu. Vestibulum vulputate Vestibulum vitae aliquam nunc. Suspendisse mollis metus ac tellus egestas pharetra. Suspendisse at viverra purus. Pellentesque nec posuere ligula, eu congue leo. Integer vulputate tempor arcu. Vestibulum vulputate

We're Awesome!

Vestibulum vitae aliquam nunc. Suspendisse mollis metus ac tellus egestas pharetra. Suspendisse at viverra purus. Pellentesque nec posuere ligula, eu congue leo. Integer vulputate tempor arcu.