On super (a, d) − P2 B H− antimagic total labeling of disjoint union of comb product graphs

Abstract

This study focuses on simple and undirected graphs. For a graph G = (V, E), a bijection λ from V (G)∪E(G) into {1, 2, ..., |V (G)|+|E(G)|} is called super (a, d)-H-antimagic total labeling of G if the total P2BH−weights, wP2BH = P v∈V (P2BH) λ(v)+P e∈E(P2BH) λ(e) form an arithmetic sequence progression starting from a and having common difference d. The graph chosen in this paper is graph from operation of comb product. Some results of the labeling of comb product can be seen at [6],[7],and [8]. The combination of two grafts G1 and G2 is denoted by G1 ∪ G2. The combination of two grafts is defined as a graph with the set of vertex V (G1) ∪ V (G2) and the set off edge E(G1) ∪ E(G2). The disjoint union of graphs, sG, is defined as a combination of each other from s copies of graph G. In other words, sG = G1 ∪ G2 ∪ G3 ∪ · · · ∪ Gs, with G1 = G2 = G3 = · · · = Gs = G. If graph G has a p vertices and q edges, then the graph sG has sp vertices and sq edges.