Super [formula omitted]-edge antimagic total labeling of a subclass of trees

Abstract

A graph labeling is a mapping that assigns numbers to graph elements. The domain can be the set of all vertices, the set of all edges or the set of all vertices and edges. A labeling in which domain is the set of vertices and edges is called a total labeling. For a graph G with the vertex set V(G) and the edge set E(G), a total labeling f:V(G)∪E(G)→{1,2,3,…,|V(G)|+|E(G)|} is called an (a,d)-edge antimagic total labeling if the set of edge weights {f(x)+f(xy)+f(y):xy∈E(G)} forms an arithmetic progression with initial term a and common difference d. An (a,d)-edge antimagic total labeling is called a super(a,d)-edge antimagic total labeling if the smallest labels are assigned to the vertices. In this paper, we investigate the super(a,d)-edge-antimagic total labeling of a subclass of trees called subdivided stars for all possible values of d, mainly d=1,3.