ON SUPER (a, d)-EAT VALUATION OF SUBDIVIDED CATERPILLAR

Özet

Let G = (V (G), E(G)) be a graph with v = |V (G)| vertices and e = |E(G)| edges. A bijective function λ : 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) = λ(x) + λ(y) + λ(xy). And, if λ(V ) = {1, 2, . . . , v} then G is super (a, d)-edge antimagic total(EAT) graph. In this paper, we determine the super (a,d)-edge antimagic total (EAT) labeling of the subdivided caterpillar for different values of the parameter d.