Pelabelan Total Super (a,d)-Sisi Antimagic Pada Graf Buah Naga

Abstract

A graph $G$ is called an $(a,d)$-edge-antimagic total labeling if there exist a one-to-one mapping $f : f(V)=\{1,2,3,...,p\} \to f(E)=\{1,2,\dots,p+q\}$ such that the edge-weights, $w(uv)=f(u)+f(v)+f(uv), uv \in E(G)$, form an arithmetic progression $\{a,a+d,a+2d,\dots,a+(q-1)d\}$, where $a>0$ and $d\ge 0$ are two fixed integers, form an arithmetic sequence with first term $a$ and common difference $d$. Such a graph $G$ is called {\it super} if the smallest possible labels appear on the vertices. In this paper we recite super $(a,d)$-edge-antimagic total labelling of connected  Dragon Fruit Graph. The result shows that Dragon Fruit Graph have a super edge antimagic total  labeling for $d\in{0,1,2}$.