arXiv:2610.35419 · v1

Antimagic Labeling of Central Digraphs Constructed from Loops

首次提交 2026-10-26 21:29

版本更新 2026-10-26 21:29

雷达观测 2026-10-29 00:36

摘要

Let $(T, \circ)$ be a loop of order $k \geq 3$ 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 $(\text{tail}, \text{head})$ and assigning labels $1, \ldots, m$ in that order and prove that $f$ is an antimagic labeling. Consequently, $D_S$ is antimagic for every loop of order $k \geq 3$, a property that depends only on $k$ and is invariant across all non-isomorphic loops of the same order.

作者备注：15 page article