SOME RESULT OF NON-COPRIME GRAPH OF INTEGERS MODULO n GROUP FOR n A PRIME POWER

Masriani, Masriani; Juliana, Rina; Syarifudin, Abdul Gazir; Wardhana, I Gede Adhitya Wisnu; Irwansyah, Irwansyah; Switrayni, Ni Wayan

doi:10.14710/jfma.v3i2.8713

Cited by 5 publications

(4 citation statements)

References 2 publications

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“…The non-coprime graph constitutes a novel method for graph representation, and it was introduced by Mansoori [7]. A non-coprime graph involves the order of the group elements as described in the following definition.…”

Section: Resultsmentioning

confidence: 99%

The Structures of Non-Coprime Graphs for Finite Groups from Dihedral Groups with Regular Composite Orders

Aulia,

Wardhana,

Irwansyah

et al. 2023

InPrime:Ind.Jour.Pure.Applied.Math

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For any finite group, the non-coprime graph of the group is a graph with vertices consisting of all non-identity elements of the group. Two different vertices are considered adjacent if their orders are not coprime, meaning their greatest common divisor (gcd) is not equal to one. Misuki provides the structure of the non-coprime graph for the dihedral group when the order is a prime power. We establish a more general property for cases where the order of the group is a regular composite number, discovering that the structure of the non-coprime graph for a dihedral group can be partitioned into some number of complete subgraphs.Keywords: dihedral group; disjoint subgraph; non-coprime graph. AbstrakUntuk sebarang grup hingga, graf non-coprime dari grup tersebut adalah graf dengan simpul yang terdiri dari semua elemen non-identitas dari grup tersebut. Dua simpul yang berbeda dianggap bertetangga jika orde mereka tidak saling prima, artinya pembagi terbesar bersama (gcd) mereka tidak sama dengan satu. Misuki memberikan struktur graf non-coprime untuk grup dihedral ketika ordenya adalah pangkat prima. Pada studi ini didapatkan sifat yang lebih umum ketika orde grup adalah bilangan komposit biasa. Didapatkan juga bahwa struktur graf non-coprime dari grup dihedral dapat dipartisi menjadi beberapa subgraf lengkap.Kata Kunci: graf non-koprima; grup dihedral; subgraph disjoin. 2020MSC: 05C25, 05C69, 20D60.

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Section: Resultsmentioning

confidence: 99%

The Structures of Non-Coprime Graphs for Finite Groups from Dihedral Groups with Regular Composite Orders

Aulia,

Wardhana,

Irwansyah

et al. 2023

InPrime:Ind.Jour.Pure.Applied.Math

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“…Furthermore, in 2007, Anderson et al [18 In addition to using graphs, one also employs them as representations of mathematical systems such as groups and rings. One uses graphs to represent groups, for example, coprime [1,2], non-coprime [3,4], relative coprime [5], power [6], commuting [7], cyclic [8], and intersection [9] graphs. Rings are represented by the zero divisor [10], prime [11], and Jacobson [12,13] graphs.…”

Section: Introductionmentioning

confidence: 99%

Topological Indices and Properties of the Prime Ideal Graph of a Commutative Ring and its Line Graph

Syarifudin,

Muchtadi-Alamsyah,

Suwastika

2024

Contemp. Math.

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Let R be a commutative ring with identity, and P be a prime ideal of R. The prime ideal graph, denoted by Γp, is the graph where the set of vertices is R/{0} and two vertices are joined by an edge if their product belongs to P. This paper will discuss topological indices and some properties of the prime ideal graph of a commutative ring and its line graph. Topological indices, such as the Wiener, first Zagreb, second Zagreb, Harary, Gutman, Schultz, and Harmonic indices, are related to the degree of vertices and the diameter of the graphs. In this paper, we also discuss the independence and domination numbers of the line graph.

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“…The factorization theorem on integers is a motivation for developing graph studies involving a ring of integers modulo 𝑛. One of the graph studies carried out was a study on non-coprime for ℤ 𝑛 [15]. In this research, we combine the properties of (Exact) Annihilating Ideal Graph of arbitrary ring with factorization of ring integer modulo 𝑛.…”

Section: Introductionmentioning

confidence: 99%

ANNIHILATING IDEAL AND EXACT ANNIHILATING IDEAL GRAPH OF RING Z_n

Susanto,

Putra

2023

BAREKENG: J. Math. & App.

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The existence of annihilator in the ring motivates the emergence of studies on Annihilating Ideal and Exact Annihilating Ideal Graphs. The purpose of this research is to describe the characteristics of an (exact) annihilating ideal of ring . The method used in this research is literature study. The results of this study discuss finiteness, adjacency, connectedness, vertices, and types of and . Furthermore, the number of vertices of an Annihilating Ideal Graph is determined by the factorization of . The adjacency of two vertices is determined by the divisibleness of . The results also show that is a subgraph of . can be represented as a union of several complete graphs.

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SOME RESULT OF NON-COPRIME GRAPH OF INTEGERS MODULO n GROUP FOR n A PRIME POWER

Cited by 5 publications

References 2 publications

The Structures of Non-Coprime Graphs for Finite Groups from Dihedral Groups with Regular Composite Orders

The Structures of Non-Coprime Graphs for Finite Groups from Dihedral Groups with Regular Composite Orders

Topological Indices and Properties of the Prime Ideal Graph of a Commutative Ring and its Line Graph

ANNIHILATING IDEAL AND EXACT ANNIHILATING IDEAL GRAPH OF RING Z_n

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