Group Distance Magic Labeling of Graphs and their Direct Product

Wasim Ashraf; Hani Shaker; Muhammad Imran; Kiki Ariyanti Sugeng

Group Distance Magic Labeling of Graphs and their Direct Product

Wasim Ashraf, Hani Shaker, Muhammad Imran, Kiki Ariyanti Sugeng

Research output: Contribution to journal › Article › peer-review

Abstract

A graph G is said to have the group distance magic labeling if there exists an abelian group H and one-one map A from the vertex set of G to the group elements such that x∈N (u) A(x) = μ for all u ∈ V, where N (u) is the open neighborhood of u and μ ∈ H is the magic constant, more specifically such graph is called H-distance magic graph. In this paper, we prove anti-prism graphs are Z_2n, Z₂× Z_n, Z₃× Z_6m, Z₄× Z_6m, and Z₆× Z_6m-distance magic graphs. This paper also concludes the group distance magic labeling of direct product of the anti-prism graphs.

Original language	English
Pages (from-to)	18-26
Number of pages	9
Journal	Utilitas Mathematica
Volume	119
Publication status	Published - 2022
Externally published	Yes

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

Cite this

@article{34a84af7c78147f4a80a12a9e6fc8755,

title = "Group Distance Magic Labeling of Graphs and their Direct Product",

abstract = "A graph G is said to have the group distance magic labeling if there exists an abelian group H and one-one map A from the vertex set of G to the group elements such that x∈N (u) A(x) = μ for all u ∈ V, where N (u) is the open neighborhood of u and μ ∈ H is the magic constant, more specifically such graph is called H-distance magic graph. In this paper, we prove anti-prism graphs are Z2n, Z2× Zn, Z3× Z6m, Z4× Z6m, and Z6× Z6m-distance magic graphs. This paper also concludes the group distance magic labeling of direct product of the anti-prism graphs.",

author = "Wasim Ashraf and Hani Shaker and Muhammad Imran and Sugeng, {Kiki Ariyanti}",

year = "2022",

language = "English",

volume = "119",

pages = "18--26",

journal = "Utilitas Mathematica",

issn = "0315-3681",

publisher = "Utilitas Mathematica Publishing Inc.",

}

TY - JOUR

T1 - Group Distance Magic Labeling of Graphs and their Direct Product

AU - Ashraf, Wasim

AU - Shaker, Hani

AU - Imran, Muhammad

AU - Sugeng, Kiki Ariyanti

PY - 2022

Y1 - 2022

N2 - A graph G is said to have the group distance magic labeling if there exists an abelian group H and one-one map A from the vertex set of G to the group elements such that x∈N (u) A(x) = μ for all u ∈ V, where N (u) is the open neighborhood of u and μ ∈ H is the magic constant, more specifically such graph is called H-distance magic graph. In this paper, we prove anti-prism graphs are Z2n, Z2× Zn, Z3× Z6m, Z4× Z6m, and Z6× Z6m-distance magic graphs. This paper also concludes the group distance magic labeling of direct product of the anti-prism graphs.

AB - A graph G is said to have the group distance magic labeling if there exists an abelian group H and one-one map A from the vertex set of G to the group elements such that x∈N (u) A(x) = μ for all u ∈ V, where N (u) is the open neighborhood of u and μ ∈ H is the magic constant, more specifically such graph is called H-distance magic graph. In this paper, we prove anti-prism graphs are Z2n, Z2× Zn, Z3× Z6m, Z4× Z6m, and Z6× Z6m-distance magic graphs. This paper also concludes the group distance magic labeling of direct product of the anti-prism graphs.

UR - http://www.scopus.com/inward/record.url?scp=85147965875&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85147965875&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85147965875

SN - 0315-3681

VL - 119

SP - 18

EP - 26

JO - Utilitas Mathematica

JF - Utilitas Mathematica

ER -

Group Distance Magic Labeling of Graphs and their Direct Product

Abstract

ASJC Scopus subject areas

Other files and links

Fingerprint

Cite this