%0 Journal Article
%T On e-Super (a, d)-Edge Antimagic Total Labeling of Total Graphs of Paths and Cycles
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A A, SAIBULLA
%A Pushpam, Roushini Leely
%D 2024
%\ 02/10/2024
%V
%N
%P -
%! On e-Super (a, d)-Edge Antimagic Total Labeling of Total Graphs of Paths and Cycles
%K graph labeling
%K Magic labeling
%K Antimagic labeling
%R 10.22049/cco.2024.28592.1625
%X A $(p, q)$-graph $G$ is {\it $(a, d)$-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.
%U https://comb-opt.azaruniv.ac.ir/article_14701_cfe2bdce583a41a5a1acd0a6017a2a0c.pdf