The First Zagreb Index, The Wiener Index, and The Gutman Index of The Power of Dihedral Group

Research on graphs combined with groups is an interesting topic in the field of combinatoric algebra where graphs are used to represent a group. One type of graph representation of a group is a power graph. A power graph of the group G is defined as a graph whose vertex set is all elements of G and...

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Main Authors: Evi Yuniartika Asmarani, Sahin Two Lestari, Dara Purnamasari, Abdul Gazir Syarifudin, Salwa Salwa, I Gede Adhitya Wisnu Wardhana
Format: Article
Language:English
Published: Mathematics Department UIN Maulana Malik Ibrahim Malang 2023-05-01
Series:Cauchy: Jurnal Matematika Murni dan Aplikasi
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Online Access:https://ejournal.uin-malang.ac.id/index.php/Math/article/view/16991
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author Evi Yuniartika Asmarani
Sahin Two Lestari
Dara Purnamasari
Abdul Gazir Syarifudin
Salwa Salwa
I Gede Adhitya Wisnu Wardhana
author_facet Evi Yuniartika Asmarani
Sahin Two Lestari
Dara Purnamasari
Abdul Gazir Syarifudin
Salwa Salwa
I Gede Adhitya Wisnu Wardhana
author_sort Evi Yuniartika Asmarani
collection DOAJ
description Research on graphs combined with groups is an interesting topic in the field of combinatoric algebra where graphs are used to represent a group. One type of graph representation of a group is a power graph. A power graph of the group G is defined as a graph whose vertex set is all elements of G and two distinct vertices a and b are adjacent if and only if  or  for a positive integer  and . In addition to mathematics, graph theory can be applied to various fields of science, one of which is chemistry, which is related to topological indices. In this study, the topological indexes will be discussed, namely the Zagreb index, the Wiener index, and the Gutman index of the power graph of the dihedral group  where  with  prime numbers and an  natural number. The method used in this research is a literature review. The results obtained from this study are the first Zagreb index, Wiener index, and Gutman index of the power graph of the dihedral group  where  where  is prime and an m natural number respectively is .
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publisher Mathematics Department UIN Maulana Malik Ibrahim Malang
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spelling doaj-art-2e02ef9bad10448ebdc3d09a406eded32025-08-20T02:13:45ZengMathematics Department UIN Maulana Malik Ibrahim MalangCauchy: Jurnal Matematika Murni dan Aplikasi2086-03822477-33442023-05-017451352010.18860/ca.v7i4.169917011The First Zagreb Index, The Wiener Index, and The Gutman Index of The Power of Dihedral GroupEvi Yuniartika Asmarani0Sahin Two Lestari1Dara Purnamasari2Abdul Gazir Syarifudin3Salwa Salwa4I Gede Adhitya Wisnu Wardhana5University of MataramUniversity of MataramUniversity of MataramInstitut Teknologi BandungUniversity of MataramUniversity of MataramResearch on graphs combined with groups is an interesting topic in the field of combinatoric algebra where graphs are used to represent a group. One type of graph representation of a group is a power graph. A power graph of the group G is defined as a graph whose vertex set is all elements of G and two distinct vertices a and b are adjacent if and only if  or  for a positive integer  and . In addition to mathematics, graph theory can be applied to various fields of science, one of which is chemistry, which is related to topological indices. In this study, the topological indexes will be discussed, namely the Zagreb index, the Wiener index, and the Gutman index of the power graph of the dihedral group  where  with  prime numbers and an  natural number. The method used in this research is a literature review. The results obtained from this study are the first Zagreb index, Wiener index, and Gutman index of the power graph of the dihedral group  where  where  is prime and an m natural number respectively is .https://ejournal.uin-malang.ac.id/index.php/Math/article/view/16991first zagreb indexwinner indexgutman indexpower graphdihedral group
spellingShingle Evi Yuniartika Asmarani
Sahin Two Lestari
Dara Purnamasari
Abdul Gazir Syarifudin
Salwa Salwa
I Gede Adhitya Wisnu Wardhana
The First Zagreb Index, The Wiener Index, and The Gutman Index of The Power of Dihedral Group
Cauchy: Jurnal Matematika Murni dan Aplikasi
first zagreb index
winner index
gutman index
power graph
dihedral group
title The First Zagreb Index, The Wiener Index, and The Gutman Index of The Power of Dihedral Group
title_full The First Zagreb Index, The Wiener Index, and The Gutman Index of The Power of Dihedral Group
title_fullStr The First Zagreb Index, The Wiener Index, and The Gutman Index of The Power of Dihedral Group
title_full_unstemmed The First Zagreb Index, The Wiener Index, and The Gutman Index of The Power of Dihedral Group
title_short The First Zagreb Index, The Wiener Index, and The Gutman Index of The Power of Dihedral Group
title_sort first zagreb index the wiener index and the gutman index of the power of dihedral group
topic first zagreb index
winner index
gutman index
power graph
dihedral group
url https://ejournal.uin-malang.ac.id/index.php/Math/article/view/16991
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