on $e$-super $(a, d)$-edge antimagic total labeling of total graphs of paths and cycles

A $(p, q)$-graph $g$ is $(a, d)$-edge antimagic total if there exists a bijection $f$ from $v(g) cup e(g)$ to ${1, 2, dots, p+q}$ such that for each edge $uv in e(g)$, the edge weight $lambda(uv) = f(u) + f(uv) + f(v)$ forms an arithmetic progression with first term $a > 0$ and common difference $d geq 0$. an $(a, d)$-edge antimagic total labeling in which the vertex labels are $1, 2, dots, p$ and edge labels are $p+1, p+2, dots, p+q$ is called a {it super} $(a, d)$-{it edge antimagic total labeling}. another variant of $(a, d)$-edge antimagic total labeling called as e-super $(a, d)$-edge antimagic total labeling in which the edge labels are $1, 2, dots, q$ and vertex labels are $q+1, q+2, dots, q+p$. in this paper, we investigate the  existence of e-super $(a, d)$-edge antimagic total labeling for total graphs of paths, copies of cycles and disjoint union of cycles.