Two types irregular labelling on dodecahedral modified generalization graph

Nurdin Hinding; Kiki A. Sugeng; Nurlindah; Timothy J. Wahyudi; Rinovia Simanjuntak

doi:10.1016/j.heliyon.2022.e11197

Two types irregular labelling on dodecahedral modified generalization graph

Nurdin Hinding, Kiki A. Sugeng, Nurlindah, Timothy J. Wahyudi, Rinovia Simanjuntak

Department of Mathematics

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

Abstract

Irregular labelling on graph is a function from component of graph to non-negative natural number such that the weight of all vertices, or edges are distinct. The component of graph is a set of vertices, a set of edges, or a set of both. In this paper we study two types of irregular labelling on dodecahedral modified generalization graph. We determined the total vertex irregularity strength and the modular irregularity strength of dodecahedral modified generalized graph. These results are important because there many classes of graph have the same structure with modified dodecahedral graphs. These results can be used to determine the total vertex irregularity strength and the modular irregularity strength of other graphs that have the similar structure with modified dodecahedral graph.

Original language	English
Article number	e11197
Journal	Heliyon
Volume	8
Issue number	11
DOIs	https://doi.org/10.1016/j.heliyon.2022.e11197
Publication status	Published - Nov 2022

Keywords

Dodecahedral graph
Irregular labelling
Modular irregularity strength
Total vertex irregularity strength

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10.1016/j.heliyon.2022.e11197

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title = "Two types irregular labelling on dodecahedral modified generalization graph",

abstract = "Irregular labelling on graph is a function from component of graph to non-negative natural number such that the weight of all vertices, or edges are distinct. The component of graph is a set of vertices, a set of edges, or a set of both. In this paper we study two types of irregular labelling on dodecahedral modified generalization graph. We determined the total vertex irregularity strength and the modular irregularity strength of dodecahedral modified generalized graph. These results are important because there many classes of graph have the same structure with modified dodecahedral graphs. These results can be used to determine the total vertex irregularity strength and the modular irregularity strength of other graphs that have the similar structure with modified dodecahedral graph.",

keywords = "Dodecahedral graph, Irregular labelling, Modular irregularity strength, Total vertex irregularity strength",

author = "Nurdin Hinding and Sugeng, {Kiki A.} and Nurlindah and Wahyudi, {Timothy J.} and Rinovia Simanjuntak",

note = "Funding Information: Dr. Nurdin Hinding was supported by Universitas Hasanuddin [ 16/E1/KPT/2020 ]. Publisher Copyright: {\textcopyright} 2022 The Authors",

year = "2022",

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doi = "10.1016/j.heliyon.2022.e11197",

language = "English",

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T1 - Two types irregular labelling on dodecahedral modified generalization graph

AU - Hinding, Nurdin

AU - Sugeng, Kiki A.

AU - Nurlindah,

AU - Wahyudi, Timothy J.

AU - Simanjuntak, Rinovia

PY - 2022/11

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N2 - Irregular labelling on graph is a function from component of graph to non-negative natural number such that the weight of all vertices, or edges are distinct. The component of graph is a set of vertices, a set of edges, or a set of both. In this paper we study two types of irregular labelling on dodecahedral modified generalization graph. We determined the total vertex irregularity strength and the modular irregularity strength of dodecahedral modified generalized graph. These results are important because there many classes of graph have the same structure with modified dodecahedral graphs. These results can be used to determine the total vertex irregularity strength and the modular irregularity strength of other graphs that have the similar structure with modified dodecahedral graph.

AB - Irregular labelling on graph is a function from component of graph to non-negative natural number such that the weight of all vertices, or edges are distinct. The component of graph is a set of vertices, a set of edges, or a set of both. In this paper we study two types of irregular labelling on dodecahedral modified generalization graph. We determined the total vertex irregularity strength and the modular irregularity strength of dodecahedral modified generalized graph. These results are important because there many classes of graph have the same structure with modified dodecahedral graphs. These results can be used to determine the total vertex irregularity strength and the modular irregularity strength of other graphs that have the similar structure with modified dodecahedral graph.

KW - Dodecahedral graph

KW - Irregular labelling

KW - Modular irregularity strength

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Two types irregular labelling on dodecahedral modified generalization graph

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Keywords

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