Book graphs are cycle antimagic
Muhammad Awais Umar, Noshad Ali, Afshan Tabassum, Basharat Rehman Ali · Open Journal of Mathematical Sciences · 2019
Let G = (V, E) be a finite simple graph with v = |V(G)| vertices and e = |E(G)| edges.Further suppose that H := {H 1 , H 2 , . . ., H t } is a family of subgraphs of G.In case, each edge of E(G) belongs to at least one of the subgraphs H i from the family H, we say G admits an edge-covering.When every subgraph H i in H is isomorphic to a given graph H, then the graph G admits an H-covering.A graph G admitting H covering is called an (a, d)-H-antimagic if there is a bijection η : V ∪ E → {1, 2, . . ., v + e} such that for each subgraph H of G isomorphic to H, the sum of labels of all the edges and vertices belongs to H constitutes an arithmetic progression with the initial term a and the common difference d.For η(V) = {1, 2, 3, . . ., v}, the graph G is said to be super (a, d)-H-antimagic and for d = 0 it is called H-supermagic.When the given graph H is a cycle C m then H-covering is called C m -covering and super (a, d)-H-antimagic labeling becomes super (a, d)-C m -antimagic labeling.In this paper, we investigate the existence of super (a, d)-C m -antimagic labeling of book graphs B n , for m = 4, n ≥ 2 and for differences d = 1, 2, 3, . . ., 13.