]>Weighted Maximum-Clique Transversal Sets of Graphs : Algorithm 1
Input: A split graph ๐บ = ( ๐ผ โˆช ๐‘„ , ๐ธ , ๐‘ค ) .
Output: A maximum-clique transversal set ๐ท of ๐บ of minimum weight.
  (1) ๐‘† = ๐ผ ;
  (2) for each vertex ๐‘ฃ โˆˆ ๐‘„   do
  (3)  ๐‘ค ๐‘ ( ๐‘ฃ ) = ๐‘ค ( ๐‘ ๐บ ( ๐‘ฃ ) ) ;
  (4) end for
  (5) for each vertex ๐‘  โˆˆ ๐ผ   do
  (6)  if   d e g ๐บ ( ๐‘  ) < ๐œ” ( ๐บ ) โˆ’ 1   then
  (7)    ๐‘† โ† ๐‘† โงต { ๐‘  } ;
  (8)   for each ๐‘ฃ โˆˆ ๐‘ ๐บ ( ๐‘  )   do
  (9)     ๐‘ค ๐‘ ( ๐‘ฃ ) = ๐‘ค ๐‘ ( ๐‘ฃ ) โˆ’ ๐‘ค ( ๐‘  ) ;
(10)   end for
(11)  end if
(12) end for
(13) Find a vertex ๐‘ฃ 1 โˆˆ ๐‘„ such that ๐‘ค ( ๐‘ฃ 1 ) = m i n { ๐‘ค ( ๐‘ฃ ) โˆฃ ๐‘ฃ โˆˆ ๐‘„ } ;
(14) Find a vertex ๐‘ฃ 2 โˆˆ ๐‘„ โงต { ๐‘ฃ 1 } such that ๐‘ค ( ๐‘ฃ 2 ) = m i n { ๐‘ค ( ๐‘ฃ ) โˆฃ ๐‘ฃ โˆˆ ๐‘„ โงต { ๐‘ฃ 1 } } ;
(15) Find a vertex ๐‘ฃ 3 โˆˆ ๐‘„ such that ๐‘ค ( ๐‘† โˆช ๐‘„ ) โˆ’ ๐‘ค ๐‘ ( ๐‘ฃ 3 ) = m i n { ๐‘ค ( ๐‘† โˆช ๐‘„ ) โˆ’ ๐‘ค ๐‘ ( ๐‘ฃ ) โˆฃ ๐‘ฃ โˆˆ ๐‘„ } ;
(16) if m i n { ๐‘ค ( ๐‘ฃ 1 ) + ๐‘ค ( ๐‘ฃ 2 ) , ๐‘ค ( ๐‘† โˆช ๐‘„ ) โˆ’ ๐‘ค ๐‘ ( ๐‘ฃ 3 ) } = ๐‘ค ( ๐‘ฃ 1 ) + ๐‘ค ( ๐‘ฃ 2 )   then
(17)   ๐ท = { ๐‘ฃ 1 , ๐‘ฃ 2 } ;
(18) else
(19)   ๐ท = { ๐‘ฃ 3 } โˆช ( ๐‘† โงต ๐‘ ๐บ ( ๐‘ฃ 3 ) ) ;
(20) end if
(21) Output the set ๐ท ;
Algorithm 1: Finding a maximum-clique transversal set of a split graph of minimum weight.