A bench of justices Gita Mittal and J R Midha directed Delhi Police to "cull down" all the circumstances under which they, along with Nitish's mother Neelam Katara, are seeking the gallows or an enhanced life sentence for Vikas, Vishal Yadav and Sukhdev Pehalwan.
"You (police) cull down all aggravating and mitigating circumstances to show us (high court bench) how your case is different from others to enhance punishment of life term to death sentence.
The court has directed the police to provide them the chart by August 1, before advancing their arguments further.
Earlier, the victim's mother, who concluded her arguments had demanded death for the three terming their offence to be of the rarest of rare.
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"The trial court as well as this court have already held that this is a case of honour killing. I want to add one thing that the honour killing falls under the the rarest of rare category of cases warranting imposition of death penalty," the counsel for Neelam Katara had told the bench.
Vikas, Vishal and Sukhdev Pehalwan are serving life term for abducting and killing Nitish Katara, a business executive and son of an IAS officer, on the intervening night of February 16-17, 2002. They did not approve of the victim's affair with Bharti, daughter of D P Yadav.