On Super (a,d)‎-Edge-Antimagic Total Labeling of Special Types of Crown Graphs

Abstract EN

For a graph G=(V,E), a bijection f from V(G)∪E(G)→{1,2,…,|V(G)|+|E(G)|} is called (a,d)-edge-antimagic total ((a,d)-EAT) labeling of G if the edge-weights w(xy)=f(x)+f(y)+f(xy),xy∈E(G), form an arithmetic progression starting from a and having a common difference d, where a>0 and d≥0 are two fixed integers.

An (a,d)-EAT labeling is called super (a,d)-EAT labeling if the vertices are labeled with the smallest possible numbers; that is, f(V)={1,2,…,|V(G)|}.

In this paper, we study super (a,d)-EAT labeling of cycles with some pendant edges attached to different vertices of the cycle.