Face antimgaic labeling of double duplication for some special graphs

Abstract

The main objective of the paper is to determine (a, d)? face antimagic labeling for the double duplication of all vertices by edges of ladder, tadpole and m-copies of path graphs. Also, if a graph G is (a, d)? face antimagic except for 3-sided faces then the double duplication of all vertices by edges of a graph G is also (a,d)-face antimagic.