Super (a,d)-$\mathcal{H}$-Antimagic Total Selimut pada Graf Shackle Kipas $F_4$

Abstract

A graph $G(V,E)$ has a $\mathcal{H}$-covering if every edge in $E$ belongs to a subgraph of $G$ isomorphic to $\mathcal{H}$. An $(a,d)$-$\mathcal{H}$-antimagic total covering is a total labeling $\lambda$ from $V(G)\cup E(G)$ onto the integers $\{1,2,3,...,|V(G)\cup E(G)|\}$ with the property that, for every subgraph $A$ of $G$ isomorphic to $\mathcal{H}$ the $\sum{A}=\sum_{v\in{V(A)}}\lambda{(v)}+ \sum_{e\in{E(A)}}\lambda{(e)}$ forms an arithmetic sequence. A graph that admits such a labeling is called an $(a,d)$-$\mathcal{H}$-antimagic total covering. In addition, if $\{\lambda{(v)}\}_{v\in{V}}=\{1,...,|V|\}$, then the graph is called $\mathcal{H}$-super antimagic graph. In this paper we study a super $(a,d)$-$\mathcal{H}$-antimagic total Covering of  Shackle of Fan $F_4$.