Identifier
Values
([],1) => ([(0,1)],2) => ([],1) => 0
([],2) => ([(0,2),(1,2)],3) => ([(0,1)],2) => 1
([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 2
([],3) => ([(0,3),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 2
([(1,2)],3) => ([(0,3),(1,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
([(0,2),(1,2)],3) => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => 2
([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(2,3)],4) => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(3,4)],5) => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
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Description
The biclique partition number of a graph.
The biclique partition number of a graph is the minimum number of pairwise edge disjoint complete bipartite subgraphs so that each edge belongs to exactly one of them. A theorem of Graham and Pollak [1] asserts that the complete graph $K_n$ has biclique partition number $n - 1$.
Map
line graph
Description
The line graph of a graph.
Let $G$ be a graph with edge set $E$. Then its line graph is the graph with vertex set $E$, such that two vertices $e$ and $f$ are adjacent if and only if they are incident to a common vertex in $G$.
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.