On a Relationship between Completely Separating Systems and Antimagic Labeling of Regular Graphs

摘要

A completely separating system (CSS) on a finite set [n] is a collection C of subsets of [n] in which for each pair a ≠ b ∈ [n], there exist A, B ∈ C such that a ∈ A, b € A and b ∈ B, a ∈ B. An antimagic labeling of a graph with p vertices and q edges is a bijection from the set of edges to the set of integers {1, 2,..., q} such that all vertex weights are pairwise distinct, where a vertex weight is the sum of labels of all edges incident with the vertex. A graph is antimagic if it has an antimagic labeling. In this paper we show that there is a relationship between CSSs on a finite set and antimagic labeling of graphs. Using this relationship we prove the antimagicness of various families of regular graphs. completely separating system, vertex antimagic edge labeling, antimagic labeling, regular graph.