Super $(a, d)-\mathcal{H}-$ antimagic total covering labeling on a graph $G=(V,E)$ is total labelling $\lambda$ on $V(G)UE(G)$ to set integers $\{1,2,3,..., |V(G)UE(G)|\}$ form an arithmetic sequence $\{a, a+d, a+2d, . . .,a+(s-1)d\}$ where $a, d$ are positive integer with $a$ is firt integer, $d$ is different, and $s$ is sum of covering. This research purposes to determine cardinality of vertex, cardinality of edge, upper limit of difference value, difference value from shackle of stacked book

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... graph.The first step is determine cardinality of vertex and cardinality of edge on shackle of stacked book graph. Then determine upperlimit if difference value and the partition from labeling on shackle of stacked book graph. So that be produced super $(a, d)-\mathcal{H}-$antimagic total covering labeling on shackle of stacked book