PRODUCT ANTIMAGIC LABELINGS IN CAYLEY DIGRAPHS OF 2-GENERATED 2-GROUPS

1. IntroductionThe concept of graph labeling was introduced by Rosa in 1967 [9]. A graphlabeling is an assignment of integers to the vertices or edges or both, subject tocertain conditions. Labeled graphs serve as useful models for a broad range ofapplications such as coding theory, X-ray crystallography, radar, astronomy, cir-cuit design, communication network addressing and data base management [5].Hence in the intervening years various labeling of graphs such as graceful label-ing, harmonious labeling, magic labeling, antimagic labeling, bimagic labeling,prime labeling, cordial labeling, mean labeling, arithmetic labeling etc., havebeen studied in over 1100 papers [5]. In [3], antimagic labelings for certain classof graphs were studied. In [6], Hartsfleld and Ringel made a conjecture on vertex-antimagic labeling and Martin Baca possed a conjecture about edge-antimagicvertex labeling [8]. Figueroa-Centeno and others have introduced multiplicativeanalogs of magic and antimagic labelings [4]. They deflne a graph