Get Math Help

GET TUTORING NEAR ME!

By submitting the following form, you agree to Club Z!'s Terms of Use and Privacy Policy

    Robertson Graph

    Image

    Image

    Basic properties

    vertex count | 19
edge count | 38
connected component count | 1

    Graph features

    asymmetric | biconnected | bridgeless | cage | class 2 | connected | cyclic | Eulerian | Hamilton-connected | Hamilton-decomposable | Hamiltonian | H-star connected | imperfect | LCF | local | noncayley | nonempty | nonplanar | no perfect matching | quartic | regular | simple | square-free | traceable | triangle-free | weakly regular

    Complement graph

    (not a named graph)

    Line graph

    (not a named graph)

    Graph degrees

    vertex degrees | 4 (19 vertices)

    Topological properties

    radius | 3
diameter | 3
girth | 5
vertex connectivity | 4
edge connectivity | 4

    Graph polynomials

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

    x^18 y^20 + 38 x^18 y^19 + 703 x^18 y^18 + 8436 x^18 y^17 + 19 x^17 y^17 + 73796 x^18 y^16 + 646 x^17 y^16 + 501296 x^18 y^15 + 10697 x^17 y^15 + ... + 48554592 x^8 + 12588360 x^7 + 2758797 x^6 + 501888 x^5 + 73815 x^4 + 8436 x^3 + 703 x^2 + 38 x + 1 (142 terms)

    y^20 + 18 y^19 + 171 y^18 + 19 x y^17 + 1121 y^17 + 323 x y^16 + 5643 y^16 + 38 x^2 y^15 + 2869 x y^15 + ... + 4067425 x^9 + 8704413 x^8 + 15702294 x^7 + 23425656 x^6 + 28091119 x^5 + 25936913 x^4 + 17211692 x^3 + 7246700 x^2 + 1437372 x (141 terms)

    Coloring properties

    chromatic number | 3
edge chromatic number | 5

    Spectrum

    (1/2 (-1 - sqrt(21)))^1 (1/2 (-1 - sqrt(17)))^2 (1/2 (-1 - sqrt(13)))^2 (-sqrt(3))^2 (1/2 (-1 - sqrt(5)))^1 (1/2 (-1 + sqrt(5)))^1 1^2 (1/2 (-1 + sqrt(13)))^2 (1/2 (-1 + sqrt(17)))^2 sqrt(3)^2 (1/2 (-1 + sqrt(21)))^1 4^1

    Associated matrices

    Associated matrices Adjacency matrix

    Associated matrices Incidence matrix

    Graph indices

    Hosoya index | 283846
Kirchhoff index | 97.94
stability index | 831104
Wiener index | 323

    Find the right fit or it’s free.

    We guarantee you’ll find the right tutor, or we’ll cover the first hour of your lesson.