I agree with you sir ...Thank you for your kind information.
Yes, you are correct ..labeling is not a bijection it is a mapping...
Moreover, Many applications are there for labeling concepts but not sure for antimagic labeling. I have searched in Google too but i couldn't get the answers for my questions. In tat thesis, they have mentioned many references but no reference is given for application purpose.. tat they have mentioned some applications just roughly... If you know the exact application for antimagic labeling pls provide me the exact evidence or references ..Thank you for your kind information.
I know the magic labeling is the special case of antimagic.. I agree with that... But i need the exact application of antimagic labeling of graphs... Please send me the exact evidence or source with correct example of antimagic labeling of graphs in real life situation... Thanks for your continuous response for this question ...Thanks a lot ...