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386562

k‑Zumkeller labeling of super subdivision of some graphs

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Last updated: 05 Jan 2025

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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.

DOI

10.1186/s42787-021-00121-y

Keywords

Zumkeller number, k-Zumkeller labeling, Complete bipartite graph, Super subdivision

Authors

First Name

M.

Last Name

Basher

MiddleName

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Affiliation

Department of Mathematics and Computer Science, Faculty of Science, Suez University, Suez, Egypt.

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Volume

29

Article Issue

1

Related Issue

50998

Issue Date

2021-01-01

Receive Date

2024-10-16

Publish Date

2021-01-01

Page Start

1

Page End

16

Print ISSN

1110-256X

Online ISSN

2090-9128

Article File

JOEMS_Volume 29_Issue 1_Pages 1-16.pdf

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https://joems.journals.ekb.eg/article_386562.html

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https://joems.journals.ekb.eg/service?article_code=386562

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386,562

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Original Article

Type Code

3,248

Publication Type

Journal

Publication Title

Journal of the Egyptian Mathematical Society

Publication Link

https://joems.journals.ekb.eg/

MainTitle

k‑Zumkeller labeling of super subdivision of some graphs

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Article

Created At

21 Dec 2024