Mathematics

CLC number: O156

On the Coprime Labelings of Hypergraph

超图的互素标号问题研究

¹ School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, Yunnan, China
² School of Mathematics and Statistics, Yangtze Normal University, Chongqing 408102, China

^† Corresponding author. E-mail: zhangshaohua@yznu.edu.cn

Received: 12 September 2024

Abstract

Graph labeling is the assignment of integers to the vertices, edges, or both, subject to certain conditions. Accordingly, hypergraph labeling is also the assignment of integers to the vertices, edges, or both, subject to certain conditions. This paper is to generalize the coprime labelings of graph to hypergraph. We give the definition of coprime labelings of hypergraph. By using Rosser-Schoenfeld's inequality and the coprime mapping theorem of Pomerance and Selfridge, we prove that some linear hypergraphs are prime.

摘要

图标号是在一定条件下将整数分配给图的顶点或边，或两者兼有，使其满足一定条件。因此超图的标号也可以在一定条件下将整数分配到超图的顶点或边上，或两者兼有，使其满足一定条件。本文将图的互素标号问题推广到超图，进一步给出了超图互素标号的定义，利用Rosser-Schoenfeld不等式和Pomerance 和Selfridge的互素映射定理，证明了一些线性超图是素超图。