Abstract:
Generalized shackle of fan graph is the development of shackle operation of fan graph F_n by connecting the some vertices in shackle of fan graph. Graph G with the cardinality of vertex p and the cardinality of edges q is called an super (a,d)-edge antimagic total labelling if there exist a bijection f: V(G)?E(G) ?{1,2,...,p+q} such that the edge-weights, w(xy)=f(x)+f(y)+f(xy),xy ?E(G), form an arithmetic sequence with first term a and common difference d. In this paper, we use pattern recognition method and we analyze the super (a,d)-edge antimagic total labeling of some generalized shackle of fan graph. The results show that Generalized Shackle of Fan Graph, GShackle(F_4,v,n) and GShackle(F_3,v,n) admit super (a,d)- edge antimagic total labelling for d?{0,1,2}.
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