Krisnawati Vira Hari, Ngurah Anak Agung Gede, Hidayat Noor, Alghofari Abdul Rouf
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Brawijaya, Jl. Veteran Malang, Jawa Timur, Indonesia.
Department of Civil Engineering, Faculty of Engineering, Universitas Merdeka Malang, Jl. Taman Agung No.1 Malang, Jawa Timur, Indonesia.
Heliyon. 2020 Nov 20;6(11):e05561. doi: 10.1016/j.heliyon.2020.e05561. eCollection 2020 Nov.
A graph is called if there exists a bijection , where , such that is a constant for every edge . Such a case, is called a super edge magic labeling of . A bipartite graph with partite sets and is called if there exists a super edge-magic labeling with the property that and . The of a graph , denoted by , is either the minimum nonnegative integer such that is super edge-magic or +∞ if there exists no such . The of a bipartite graph , denoted by , is either the minimum nonnegative integer such that is consecutively super edge-magic or +∞ if there exists no such . In this paper, we study the super edge-magic deficiency of some graphs. We investigate the (consecutively) super edge-magic deficiency of forests with two components. We also investigate the super edge-magic deficiency of a 2-regular graph and join product of with an isolated vertex.
若存在一个双射 ，其中 ，使得对于每条边 ， 为常数，则称该图为 。在这种情况下， 称为 的超边魔法标号。若存在一个超边魔法标号 ，使得 且 ，则具有顶点集 和 的二分图 称为 。图 的超边魔法亏度，记为 ，要么是使得 为超边魔法的最小非负整数 ，要么若不存在这样的 则为 +∞。二分图 的连续超边魔法亏度，记为 ，要么是使得 为连续超边魔法的最小非负整数 ，要么若不存在这样的 则为 +∞。在本文中，我们研究一些图的超边魔法亏度。我们研究具有两个分支的森林的（连续）超边魔法亏度。我们还研究 2 - 正则图 以及 与一个孤立顶点的联积的超边魔法亏度。
