Identifier
Values
([],1) => ([(0,1)],2) => ([(1,2)],3) => 2
([],2) => ([(0,2),(1,2)],3) => ([(1,3),(2,3)],4) => 2
([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => ([(1,2),(1,3),(2,3)],4) => 3
([],3) => ([(0,3),(1,3),(2,3)],4) => ([(1,4),(2,4),(3,4)],5) => 2
([(1,2)],3) => ([(0,3),(1,2),(1,3),(2,3)],4) => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
([(0,2),(1,2)],3) => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
([(2,3)],4) => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
([(1,3),(2,3)],4) => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
([(0,3),(1,3),(2,3)],4) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
([(0,3),(1,2)],4) => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 3
([(1,2),(1,3),(2,3)],4) => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
([(0,3),(1,2),(1,3),(2,3)],4) => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 4
([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
([],0) => ([],1) => ([],2) => 1
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Description
The Hadwiger number of the graph.
Also known as clique contraction number, this is the size of the largest complete minor.
Map
vertex addition
Description
Adds a disconnected vertex to a graph.
Map
cone
Description
The cone of a graph.
The cone of a graph is obtained by joining a new vertex to all the vertices of the graph. The added vertex is called a universal vertex or a dominating vertex.