Total balanced antimagic labeling
Abstract
Let \(G\) be a graph. We introduce the balanced antimagic labeling as an analogue to the antimagic labeling. A \(k\)-total balanced antimagic labelling is a map \(c\colon V (G)\cup E(G) \to \{1,2,\ldots,k\}\) such that: the label classes differ in size by at most one, each vertex \(x\) is assigned the weight \(w(x)={c}(x)+\sum\limits_{x\in e}{c}(e)\), and \(w(x)\neq w(y)\) for \(x\neq y\). We present several properties of balanced antimagic labeling. We also derive such a labeling for complete graphs and complete bipartite graphs.
Fields of Study & Subjects
Graph Labeling and Dimension Problems
Advanced Graph Theory Research
Advanced Mathematical Theories
Publication details
- Journal / source
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume
- 129
- Pages
- 57–62
- Publication date
- 26 January 2026