On super [formula omitted]-[formula omitted]-antimagic total labeling of disjoint union of cycles

Abstract

Let H and G be finite simple graphs where every edge of G belongs to at least one subgraph that is isomorphic to H. An (a,d)-H-antimagic total labeling of a graph G is a bijection f:V(G)∪E(G)→{1,2,…,|V(G)|+|E(G)|} such that for all subgraphs H′ isomorphic to H, the H-weights, w(H′)=∑v∈V(H′)f(v)+∑uv∈E(H′)f(uv) form an arithmetic progression {a,a+d,…,a+(k−1)d} where a>0,d≥0 are two fixed integers and k is the number of subgraphs of G isomorphic to H. Moreover, if the vertex set V(G) receives the minimum possible labels {1,2,…,|V(G)|}, then f is called a super(a,d)-H-antimagic total labeling. In this paper we study super (a,d)-Cn-antimagic total labeling of a disconnected graph, namely mCn.