Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 10 4 2025 12 01 On $e$-super $(a, d)$-edge antimagic total labeling of total graphs of paths and cycles 787 802 14701 10.22049/cco.2024.28592.1625 EN A. Saibulla Department of Mathematics and Actuarial Science, B.S. Abdur Rahman Crescent Institute of Science and Technology, Chennai - 600048, Tamil Nadu, India P. Roushini Leely Pushpam Department of Mathematic, D.B. Jain College, Chennai - 600097, Tamil Nadu, India Journal Article 2023 04 20 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. https://comb-opt.azaruniv.ac.ir/article_14701_37f7faae4e12bbca5890cfdaa8595a6b.pdf