D Nivedha, S Devi Yamini
Vellore Institute of Technology, Chennai, Tamil Nadu, India.
Heliyon. 2024 Jan 5;10(2):e24002. doi: 10.1016/j.heliyon.2024.e24002. eCollection 2024 Jan 30.
Given a graph , a function of assigning distinct labels to such that , ∀ is an antimagic labeling of where indicates the vertex sum obtained by summing up all the labels assigned to the edges incident on the vertex . Let , , be connected graphs such that . A new graph is constructed from , , by adding all possible edges between the end vertices of and , . The resulting graph is called the generalized edge corona of and which is denoted as . We prove ⋄ is antimagic under certain conditions using an algorithmic approach where has only one vertex of maximum degree three (excluding spider graphs containing uneven legs) and , .
给定一个图，一个为其顶点分配不同标签的函数，使得对于所有顶点 ， ，其中 表示通过对与该顶点相关联的所有边所分配的标签求和得到的顶点和。设 、 、 为连通图，使得 。通过在 和 的端点之间添加所有可能的边，从 、 、 构造一个新图。得到的图称为 和 的广义边冠，记为 。我们使用一种算法方法证明在某些条件下 是反魔法的，其中 只有一个最大度为三的顶点（不包括腿不均匀的蜘蛛图），且 ， 。
