Szczegóły publikacji
Opis bibliograficzny
$E_A$-cordial labeling of graphs and its implications for A-antimagic labeling of trees / Sylwia CICHACZ // Discrete Mathematics ; ISSN 0012-365X. — 2025 — vol. 348 iss. 9 art. no. 114493, s. 1–6. — Bibliogr. s. 6, Abstr. — Publikacja dostępna online od: 2025-03-20
Autor
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 159235 |
|---|---|
| Data dodania do BaDAP | 2025-05-15 |
| Tekst źródłowy | URL |
| DOI | 10.1016/j.disc.2025.114493 |
| Rok publikacji | 2025 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Discrete Mathematics |
Abstract
If A is a finite Abelian group, then a labeling f:E(G)→A of the edges of some graph G induces a vertex labeling on G; the vertex u receives the label ∑v∈N(u)f(uv), where N(u) is an open neighborhood of the vertex u. A graph G is EA-cordial if there is an edge-labeling such that (1) the edge label classes differ in size by at most one and (2) the induced vertex label classes differ in size by at most one. Such a labeling is called EA-cordial. In the literature, so far only EA-cordial labeling in cyclic groups has been studied. Kaplan, Lev, and Roditty studied the corresponding problem. Namely, they introduced A⁎-antimagic labeling as a generalization of antimagic labeling [11]. Simply saying, for a tree of order |A| the A⁎-antimagic labeling is such EA-cordial labeling that the label 0 is prohibited on the edges. In this paper, we give necessary and sufficient conditions for paths to be EA-cordial for any cyclic A. We also show that the conjecture for A⁎-antimagic labeling of trees posted in [11] is not true. © 2025 Elsevier B.V.
