Super ( a , d ) - C_4 -antimagicness of book graphs
Muhammad Awais Umar, Malik Anjum Javed, Mujtaba Hussain, Basharat Rehman Ali · Open Journal of Mathematical Sciences · 2018
Let G = (V, E) be a finite simple graph with |V (G)| vertices and |E(G)| edges.An edge-covering of G is a family of subgraphs H 1 , H 2 , . . ., Ht such that each edge of E(G) belongs to at least one of the subgraphs H i , i = 1, 2, . . ., t.If every subgraph H i 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|} such that for each subgraph H of G isomorphic to H, the sum of labels of all the edges and vertices belonged to H constitutes an arithmetic progression with the initial term a and the common difference d.For f (V ) = {1, 2, 3, . . ., |V (G)|}, the graph G is said to be super (a, d)-H-antimagic and for d = 0 it is called H-supermagic.In this paper, we investigate the existence of super (a, d)-C 4 -antimagic labeling of book graphs, for difference d = 0, 1 and n ≥ 2.