Pelabelan Total Super $(a,d)$-Sisi Antimagic pada Graf Shackle Fan Berorder 5

Abstract

et $G$ be a simple graph of order $p$ and size $q$. The graph $G$ is called an {\it $(a,d)$-edge-antimagic total graph} if there exist a bijection $f : V(G)\cup E(G) \to \{1,2,\dots,p+q\}$ such that the edge-weights, $w(uv)=f(u)+f(v)+f(uv), uv \in E(G)$, form an arithmetic sequence with first term $a$ and common difference $d$. Such a graph is called {\it super} if the smallest possible labels appear on the vertices. In this paper we study a super edge-antimagicness of generalized shackle of fan of order five, denoted by $gshack(F_5,e,n)$. The result shows that the graph $gshack(F_5,e,n)$ admits a super $(a,d)$-edge antimagic total labeling for some feasible $d\le 2$.