Golomb Graph
vertex count | 10 edge count | 18 connected component count | 1
apex | asymmetric | biconnected | bridgeless | chromatically nonunique | class 1 | connected | cyclic | determined by resistance | determined by spectrum | dominating nonunique | fully reconstructible in C^1 | graceful | Hamiltonian | imperfect | linklessly embeddable | map | multigraphic | noncayley | nonempty | noneulerian | nongeometric | pancyclic | perfect matching | planar | polyhedral | projective planar | rigid | simple | switchable | traceable | uniquely embeddable | unit-distance
(not a named graph)
(not a named graph)
vertex degrees | 3 (6 vertices) | 4 (3 vertices) | 6 (1 vertex)
radius | 2 diameter | 3 girth | 3 vertex connectivity | 3 edge connectivity | 3
(x^3 + x^2 - 2 x - 1)^2 (x^4 - 2 x^3 - 11 x^2 + 8 x + 27)
x^9 y^9 + 18 x^9 y^8 + 153 x^9 y^7 + 809 x^9 y^6 + 2949 x^9 y^5 + 7749 x^9 y^4 + 14841 x^9 y^3 + 20265 x^9 y^2 + 18228 x^9 y + 8405 x^9 + 7 x^8 y^7 + ... + 6 x^4 y^3 + 105 x^4 y^2 + 813 x^4 y + 2949 x^4 + 6 x^3 y^2 + 111 x^3 y + 809 x^3 + 7 x^2 y + 153 x^2 + 18 x + 1 (48 terms)
x^9 + 9 x^8 + 7 x^7 y + 38 x^7 + 6 x^6 y^2 + 50 x^6 y + 102 x^6 + 6 x^5 y^3 + 51 x^5 y^2 + 174 x^5 y + 195 x^5 + 6 x^4 y^4 + 51 x^4 y^3 + 201 x^4 y^2 + ... + 582 x y^3 + 538 x y^2 + 262 x y + 40 x + y^9 + 9 y^8 + 38 y^7 + 101 y^6 + 189 y^5 + 258 y^4 + 248 y^3 + 148 y^2 + 40 y (47 terms)
chromatic number | 4 edge chromatic number | 6
(root of 27 + 8 x - 11 x^2 - 2 x^3 + x^4 near x = -2.13317)^1 (root of -1 - 2 x + x^2 + x^3 near x = -1.80194)^2 (root of 27 + 8 x - 11 x^2 - 2 x^3 + x^4 near x = -1.67592)^1 (root of -1 - 2 x + x^2 + x^3 near x = -0.445042)^2 (root of -1 - 2 x + x^2 + x^3 near x = 1.24698)^2 (root of 27 + 8 x - 11 x^2 - 2 x^3 + x^4 near x = 1.96432)^1 (root of 27 + 8 x - 11 x^2 - 2 x^3 + x^4 near x = 3.84477)^1
Hosoya index | 469 Kirchhoff index | 29.74 stability index | 369 Wiener index | 75