On the (Consecutively) Super Edge-Magic Deficiency of Subdivision of Double Stars. (9th December 2020) - Krisnawati, Vira Hari; Ngurah, Anak Agung Gede; Hidayat, Noor; Alghofari, Abdul Rouf
Abstract : Let G be a finite, simple, and undirected graph with vertex set V G and edge set E G . A super edge-magic labeling of G is a bijection f : V G ∪ E G ⟶ 1, 2, …, V G + E G such that f V G = 1, 2, …, V G and f u + f u v + f v is a constant for every edge u v ∈ E G . The super edge-magic labeling f of G is called consecutively super edge-magic if G is a bipartite graph with partite sets A and B such that f A = 1, 2, …, A and f B = A + 1, A + 2, …, V G . A graph that admits (consecutively) super edge-magic labeling is called a (consecutively) super edge-magic graph. The super edge-magic deficiency of G, denoted by μ s G, is either the minimum nonnegative integer n such that G ∪ n K 1 is super edge-magic or + ∞ if there exists no such n . The consecutively super edge-magic deficiency of a graph G is defined by a similar way. In this paper, we investigate the (consecutively) super edge-magic deficiency of subdivision of double stars. We show that, some of them have zero (consecutively) super edge-magic deficiency.