TY - JOUR
ID - 14701
TI - On e-Super (a, d)-Edge Antimagic Total Labeling of Total Graphs of Paths and Cycles
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - A, SAIBULLA
AU - Pushpam, Roushini Leely
AD - Department of Mathematics and Actuarial Science, B.S. Abdur Rahman Crescent Institute of Science and Technology.
AD - Department of Mathematic, D.B. Jain College, Chennai - 600097, Tamil Nadu, India
Y1 - 2024
PY - 2024
VL -
IS -
SP -
EP -
KW - graph labeling
KW - Magic labeling
KW - Antimagic labeling
DO - 10.22049/cco.2024.28592.1625
N2 - 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.
UR - https://comb-opt.azaruniv.ac.ir/article_14701.html
L1 - https://comb-opt.azaruniv.ac.ir/article_14701_cfe2bdce583a41a5a1acd0a6017a2a0c.pdf
ER -