On super (a, d)-eat valuation of subdivided caterpillar

Abstract

Let G = (V (G), E(G)) be a graph with v = |V (G)| vertices and e = |E(G)| edges. A bijective function ? : V (G) ? E(G) ? {1, 2, . . . , v + e} is called an (a, d)- edge antimagic total (EAT) labeling(valuation) if the weight of all the edges {w(xy) : xy ? E(G)} form an arithmetic sequence starting with first term a and having common difference d, where w(xy) = ?(x) + ?(y) + ?(xy). And, if ?(V ) = {1, 2, . . . , v} then G is super (a, d)-edge antimagic total(EAT) graph. In this paper, we determine the süper (a,d)-edge antimagic total (EAT) labeling of the subdivided caterpillar for different values of the parameter d.