Step by step solutions marketing image
Step-by-Step Solutions with Pro
Get a step ahead with your homework
12-wheel graph

Input interpretation

12-wheel graph

Image

Image

Notation

W_12

Alternate names

(11, 1)-cone graph | (1, 11)-Jahangir graph | 12-Halin graph 26

Basic properties

vertex count | 12 edge count | 22 connected component count | 1

Graph features

apex | asymmetric | biconnected | bridgeless | class 1 | cone | connected | cyclic | graceful | Halin | Hamilton-connected | Hamiltonian | H-star connected | imperfect | Jahangir | noncayley | nonempty | noneulerian | pancyclic | perfect matching | planar | polyhedral | projective planar | self-dual | simple | traceable | uniquely colorable | wheel

Complement graph

12-wheel complement graph

Dual graph

12-wheel graph

Line graph

(not a named graph)

Graph degrees

vertex degrees | 3 (11 vertices) | 11 (1 vertex)

Topological properties

radius | 1 diameter | 2 girth | 3 vertex connectivity | 3 edge connectivity | 3

Graph polynomials

Characteristic polynomial

(x^2 - 2 x - 11) (x^5 + x^4 - 4 x^3 - 3 x^2 + 3 x + 1)^2

Rank polynomial

x^11 y^11 + 22 x^11 y^10 + 231 x^11 y^9 + 1529 x^11 y^8 + 7095 x^11 y^7 + 24266 x^11 y^6 + 62535 x^11 y^5 + 121748 x^11 y^4 + 176132 x^11 y^3 + 181280 x^11 y^2 + ... + 2057 x^4 y + 7095 x^4 + 11 x^3 y^2 + 220 x^3 y + 1529 x^3 + 11 x^2 y + 231 x^2 + 22 x + 1 (68 terms)

Tutte polynomial

x^11 + 11 x^10 + 11 x^9 y + 55 x^9 + 11 x^8 y^2 + 99 x^8 y + 165 x^8 + 11 x^7 y^3 + 132 x^7 y^2 + 396 x^7 y + 330 x^7 + 11 x^6 y^4 + 154 x^6 y^3 + ... + 100 x y + 10 x + y^11 + 11 y^10 + 55 y^9 + 165 y^8 + 330 y^7 + 462 y^6 + 462 y^5 + 330 y^4 + 165 y^3 + 55 y^2 + 10 y (67 terms)

Coloring properties

chromatic number | 4 edge chromatic number | 11

Spectrum

(-2.4641)^1 (-1.91899)^2 (-1.30972)^2 (-0.28463)^2 0.83083^2 1.68251^2 4.4641^1

Associated matrices

Adjacency matrix

Associated matrices Adjacency matrix

Incidence matrix

Associated matrices Incidence matrix

Graph indices

Hosoya index | 1178 Kirchhoff index | 48.04 stability index | 650 Wiener index | 110
POWERED BY THE WOLFRAM LANGUAGE