On Super (a,d)-Edge Antimagic Total Labeling of Some Generalized Shackle of Fan Graph

Abstract

Generalized shackle of fan graph is the development of shackle operation of fan graph 𝑭𝒏 by connecting the some vertices in shackle of fan graph. Graph G with the cardinality of vertex p and the cardinality of edges q is called an super (𝒂, 𝒅)−edge antimagic total labelling if there exist a bijection 𝒇: 𝑽(𝑮) ∪ 𝑬(𝑮) → {𝟏, 𝟐, . . . , 𝒑+ 𝒒} such that the edge-weights, 𝒘(𝒙𝒚) = 𝒇(𝒙) +𝒇(𝒚)+ 𝒇(𝒙𝒚), 𝒙𝒚 ∈ 𝑬(𝑮), form an arithmetic sequence with first term a and common difference d. In this paper, we use pattern recognition method and we analyze the super (a,d)-edge antimagic total labeling of some generalized shackle of fan graph. The results show that Generalized Shackle of Fan Graph, GShackle(𝑭𝟒, 𝒗, 𝒏) and GShackle(𝑭𝟑, 𝒗, 𝒏) admit super (a,d)- edge antimagic total labelling for 𝒅 ∈ {𝟎, 𝟏, 𝟐}.