Generalized perimantanes diamondoid structure and their edge-based metric dimensions

Al-Nashri Al-Hossain Ahmad; Ali Ahmad; Al-Nashri Al-Hossain Ahmad; Ali Ahmad

doi:10.3934/math.2022653

AIMS Mathematics

2022, Volume 7, Issue 7: 11718-11731. doi: 10.3934/math.2022653

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Research article

Generalized perimantanes diamondoid structure and their edge-based metric dimensions

Al-Nashri Al-Hossain Ahmad ¹,
Ali Ahmad ^{2
,
,}

1.
Department of Mathematics, AL Qunfudha University College, Umm AL-Qura University, Saudi Arabia
2.
College of Computer Science and Information Technology, Jazan University, Jazan, Saudi Arabia

Received: 24 February 2022 Revised: 28 March 2022 Accepted: 06 April 2022 Published: 18 April 2022
MSC : 05C09, 05C12, 05C92

Due to its superlative physical qualities and its beauty, the diamond is a renowned structure. While the green-colored perimantanes diamondoid is one of a higher diamond structure. Motivated by the structure's applications and usage, we look into the edge-based metric parameters of this structure. In this draft, we have discussed edge metric dimension and their generalizations for the generalized perimantanes diamondoid structure and proved that each parameter depends on the copies of original or base perimantanes diamondoid structure and changes with the parameter $ {\lambda} $ or its number of copies.
- mixed metric dimension,
- edge metric dimension,
- generalized perimantanes diamondoids,
- diamond structure,
- edge resolving set
Citation: Al-Nashri Al-Hossain Ahmad, Ali Ahmad. Generalized perimantanes diamondoid structure and their edge-based metric dimensions[J]. AIMS Mathematics, 2022, 7(7): 11718-11731. doi: 10.3934/math.2022653

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Abstract

Due to its superlative physical qualities and its beauty, the diamond is a renowned structure. While the green-colored perimantanes diamondoid is one of a higher diamond structure. Motivated by the structure's applications and usage, we look into the edge-based metric parameters of this structure. In this draft, we have discussed edge metric dimension and their generalizations for the generalized perimantanes diamondoid structure and proved that each parameter depends on the copies of original or base perimantanes diamondoid structure and changes with the parameter $ {\lambda} $ or its number of copies.

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