On Magic Distinct Labellings of Simple Graphs

Autor:	Guoce Xin, Xinyu Xu, Chen Zhang, Yueming Zhong
Jazyk:	angličtina
Rok vydání:	2021
Předmět:	Computational Mathematics Algebra and Number Theory Astrophysics::High Energy Astrophysical Phenomena FOS: Mathematics Physics::Atomic and Molecular Clusters Mathematics - Combinatorics Primary 05A19 Secondary 11D04 05C78 Combinatorics (math.CO)
Popis:	A magic labelling of a graph $G$ with magic sum $s$ is a labelling of the edges of $G$ by nonnegative integers such that for each vertex $v\in V$, the sum of labels of all edges incident to $v$ is equal to the same number $s$. Stanley gave remarkable results on magic labellings, but the distinct labelling case is much more complicated. We consider the complete construction of all magic labellings of a given graph $G$. The idea is illustrated in detail by dealing with three regular graphs. We give combinatorial proofs. The structure result was used to enumerate the corresponding magic distinct labellings. 14 pages, 6 figures
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b3e688313a630e3c4bb53bcaf1e24792 http://arxiv.org/abs/2107.03161 Zobrazit plný text záznamu