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

A. Raheem, M. Javaid, M. A. Umar, G. C. Lau

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Abstract

Let G = (V (G);E(G)) be a graph with v = jV (G)j vertices and e = jE(G)j edges. A bijective function  : V (G) [ E(G) $ f1; 2; : : : ; v + eg is called an (a; d)- edge antimagic total (EAT) labeling(valuation) if the weight of all the edges fw(xy) : xy 2 E(G)g form an arithmetic sequence starting with rst term a and having common dierence d, where w(xy) = (x) + (y) + (xy). And, if (V ) = f1; 2; : : : ; vg 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 dierent values of the parameter d.

Keywords

caterpillar, subdivided caterpillar, super(a; d)-EAT graph.