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 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.