Recently I bought this plant. what is the name and how to propagate please?

Question

http://i238.photobucket.com/albums/ff203/moorthi4/DSCN1055.jpg

Answer 1

You might enjoy the website below it's very interesting. I've included an excerpt.
A Brief History of Dianthus
http://hortparadise.unl.edu/Newsrelease/News/dianthusII.htm
Europe to England and eventually to colonial America, picking up a variety of intriguing names along the way. Known variously as sweet william, pinks, gillyflower, cottage pink, carnation and clove pink, Dianthus species became an integral part of gardens, due to their charming forms, colors and sometimes heady fragrances. People also used the flowers for flavorings, in wine, soups, sauces and jams.
When growing Dianthus in the garden, keep these tips in mind:
THERE IS A LIST OF HOW TO's
Same link as above

The Dianthus species are mostly perennial herbs, a few are annual or biennial, and some are low subshrubs with woody basal stems.
http://www.mygarden.net.au/flex/dianthus/124/
How to propogate will depend on what kind you have. If it's annual no need to bother. All that I know is if it's perennial it will self seed and spread thru out the garden

Answer 2

Yes, that's a dianthus.
I've had success separating the plant at the roots, ie a plant in a 6in pot becomes 2 with root sections about 3 in. This worked well for me when I wanted to tuck the plant in small spots in my window baskets.

Answer 3

I think it a Dianthus.
http://www.fernlea.com/fall/variety/dianthus.htm
I think they have seeds to propagate. You may try rooting a cutting.
http://www.gardenersnet.com/flower/dianthus.htm