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Antimagic Labeling of Central Digraphs Constructed from Loops
Abstract
Let (T, ∘) be a loop of order k ≥ 3 and DS* the loopless central digraph obtained from the associated central digraph DS by removing the k self-loops at the diagonal vertices. We construct an explicit arc-labeling f of DS* ordering all arcs lexicographically by (tail, head) and assigning labels 1, …, m in that order and prove that f is an antimagic labeling. Consequently, DS is antimagic for every loop of order k ≥ 3, a property that depends only on k and is invariant across all non-isomorphic loops of the same order.
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BibTeX
@misc{rawat2026antimagic,
title = {{Antimagic Labeling of Central Digraphs Constructed from Loops}},
author = {Raja Rawat},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35419},
eprint = {2610.35419},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35419},
}
RIS
TY - UNPB
TI - Antimagic Labeling of Central Digraphs Constructed from Loops
AU - Raja Rawat
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35419
UR - https://arxiv.org/abs/2610.35419
AB - Let (T, ∘) be a loop of order k ≥ 3 and D_S^* the loopless central digraph obtained from the associated central digraph D_S by removing the k self-loops at the diagonal vertices. We construct an explicit arc-labeling f of D_S^* ordering all arcs lexicographically by (tail, head) and assigning labels 1, …, m in that order and prove that f is an antimagic labeling. Consequently, D_S is antimagic for every loop of order k ≥ 3, a property that depends only on k and is invariant across all non-isomorphic loops of the same order.
ER -