K_7-C_4

7-graph 993 | projective planar forbidden graph 26

vertex count | 7 edge count | 17 connected component count | 1

square and three singletons

(not a named graph)

vertex degrees | 4 (4 vertices) | 6 (3 vertices)

radius | 1 diameter | 2 girth | 3 vertex connectivity | 3 edge connectivity | 4

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

x^6 y^11 + 17 x^6 y^10 + 136 x^6 y^9 + 680 x^6 y^8 + 2376 x^6 y^7 + 6136 x^6 y^6 + 12059 x^6 y^5 + 18253 x^6 y^4 + 21201 x^6 y^3 + 18415 x^6 y^2 + 11115 x^6 y + ... + 2131 x^4 y + 2072 x^4 + 10 x^3 y^3 + 72 x^3 y^2 + 308 x^3 y + 661 x^3 + 19 x^2 y + 136 x^2 + 17 x + 1 (36 terms)

x^6 + 11 x^5 + 19 x^4 y + 47 x^4 + 10 x^3 y^3 + 42 x^3 y^2 + 118 x^3 y + 97 x^3 + 2 x^2 y^6 + 12 x^2 y^5 + 48 x^2 y^4 + 120 x^2 y^3 + 225 x^2 y^2 + 247 x^2 y + ... + 192 x y + 36 x + y^11 + 6 y^10 + 21 y^9 + 52 y^8 + 102 y^7 + 165 y^6 + 226 y^5 + 255 y^4 + 225 y^3 + 132 y^2 + 36 y (35 terms)

chromatic number | 5 edge chromatic number | 6

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

(0 | 0 | 1 | 0 | 1 | 1 | 1 0 | 0 | 0 | 1 | 1 | 1 | 1 1 | 0 | 0 | 0 | 1 | 1 | 1 0 | 1 | 0 | 0 | 1 | 1 | 1 1 | 1 | 1 | 1 | 0 | 1 | 1 1 | 1 | 1 | 1 | 1 | 0 | 1 1 | 1 | 1 | 1 | 1 | 1 | 0)

(1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1)

Hosoya index | 136 Kirchhoff index | 8.133 stability index | 76 Wiener index | 25