Solairaju and Chithra introduced a new type of labeling of a graph G with p vertices and q edges called an edge odd graceful labeling if there is a bijection f from the edges of the graph to the set { 1 , 3 , … , 2 q ? 1 } such that, when each vertex is assigned the sum of all edges incident to it m o d 2 k , where k = max ( p , q ) , the resulting vertex labels are distinct. In this paper we proved necessary and sufficient conditions for some path and cycle related graphs to be edge odd graceful such as: Friendship graphs, Wheel graph, Helm graph, Web graph, Double wheel graph, Gear graph, Fan graph, Double fan graph and Polar grid graph.
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机译：Solairaju和Chithra引入了一种新的带有p个顶点和q个边的图G的标注，称为“边奇数优雅标注”，如果从图的边到集合{1，3，…，2 q？ 1}，这样，当为每个顶点分配入射到其的所有边的总和m o d 2 k，其中k = max（p，q）时，得到的顶点标记是不同的。在本文中，我们证明了某些与路径和循环有关的图成为边缘奇妙的条件的充要条件，例如：友谊图，轮图，Helm图，Web图，双轮图，齿轮图，扇形图，双扇形图和极坐标图。
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