On $k$-layered numbers and some labeling related to $k$-layered numbers

F. Jokar

On $k$-layered numbers and some labeling related to $k$-layered numbers

Number Theory 2021-04-20 v8 Combinatorics

Authors: F. Jokar

Abstract

In this paper, first, we define and investigate $k$ -layered numbers, which are a generalization of Zumkeller numbers. After that, we generalize the concept of Zumkeller labeling and Zumkeller cordial labeling to $k$ -layered labeling and $k$ -layered cordial labeling, respectively. Moreover, we prove that every simple graph admits Zumkeller labeling, Zumkeller cordial labeling, 3-layered labeling, 3-layered cordial labeling, 4-layered labeling and 4-layered cordial labeling.

Keywords

k-layered numbers Zumkeller numbers Zumkeller labeling k-layered labeling cordial labeling simple graphs

Cite

@article{arxiv.2003.11309,
  title  = {On $k$-layered numbers and some labeling related to $k$-layered numbers},
  author = {F. Jokar},
  journal= {arXiv preprint arXiv:2003.11309},
  year   = {2021}
}

Comments

There exists some typo mistakes in some of proofs

On $k$-layered numbers and some labeling related to $k$-layered numbers

Abstract

Keywords

Cite

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