A simple graph $$G=(V,E)$$ is said to be k-Zumkeller graph if there is an injective function f from the vertices of G to the natural numbers N such that when each edge $$xy\in E$$ is assigned the label f(x)f(y), the resulting edge labels are k distinct Zumkeller numbers. In this paper, we show that the super subdivision of path, cycle, comb, ladder, crown, circular ladder, planar grid and prism are k-Zumkeller graphs.

中文翻译：

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一些图的超细分的k -Zumkeller标记

如果存在从G的顶点到自然数N的内推函数f使得当每个边$$ xy \ in E时，一个简单的图$$ G =（V，E）$$被称为k-Zumkeller图。 $$为标签f（x）f（y）分配，结果边缘标签为k个不同的Zumkeller编号。在本文中，我们证明了路径，循环，梳形，梯形，冠形，圆形梯形，平面网格和棱镜的超细分是k-Zumkeller图。