Vertex-antimagic Total Labeling of the Union of Suns

Andrea Parestu1, Denny R. Silaban1, Kiki A. Sugeng1
1Department of Mathematics, Faculty of Mathematics and Sciences, University of Indonesia Depok 16424, Indonesia

Abstract

Let \( G = (V, E) \) be a graph with \( V(G) \) as a set of vertices and \( E(G) \) as a set of edges, where \( n = |V(G)| \) and \( e = |E(G)| \). A graph \( G = (V, E) \) is said to be \((a, d)\)-vertex antimagic total if there exist positive integers \( a \), \( d \), and a bijection \( \lambda \) from \( V(G) \cup E(G) \) to the set of consecutive integers \(\{1, 2, \ldots, n+e\}\) such that the weight of vertices forms an arithmetical progression with initial term \( a \) and common difference \( d \). In this paper, we will give \((a, d)\)-vertex antimagic total labeling of disconnected graphs, which consists of the union of \( t \) suns for \( d \in \{1, 2, 3, 4, 6\} \).

Keywords: Vertex antimagic total labeling, sun graph.