k‑Zumkeller labeling of super subdivision of some graphs | ||||
| Journal of the Egyptian Mathematical Society | ||||
| Volume 29, Issue 1, 2021, Page 1-16 PDF (2.74 MB) | ||||
| Document Type: Original Article | ||||
| DOI: 10.1186/s42787-021-00121-y | ||||
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| Author | ||||
| M. Basher* | ||||
| Department of Mathematics and Computer Science, Faculty of Science, Suez University, Suez, Egypt. | ||||
| Abstract | ||||
| 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 ∈ 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. | ||||
| Keywords | ||||
| Zumkeller number; k-Zumkeller labeling; Complete bipartite graph; Super subdivision | ||||
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