The matrix Jacobson graph of finite commutative rings

Humaira, Siti; Astuti, Pudji; Muchtadi-Alamsyah, Intan; Erfanian, Ahmad

doi:10.5614/ejgta.2022.10.1.12

Cited by 2 publications

(2 citation statements)

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“…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. Vertices and edges in each type of graph are determined based on the definitions of the respective graphs [14][15][16].…”

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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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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“…Some graphs that can be used to represent a group are coprime graph [2], non-coprime graph [3], power graph [4], and intersection graph [5]. Graphs that can be used to represent a ring are zero divisor graph [6], prime graph [7], and Jacobson graph [8]. In addition, graphs that can be used to represent a module are annihilator graphs [9].…”

Section: Introductionmentioning

confidence: 99%

On Properties of Prime Ideal Graphs of Commutative Rings

Kurnia,

Abrar,

Syarifudin

et al. 2023

BAREKENG: J. Math. & App.

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The prime ideal graph of in a finite commutative ring with unity, denoted by , is a graph with elements of as its vertices and two elements in are adjacent if their product is in . In this paper, we explore some interesting properties of . We determined some properties of such as radius, diameter, degree of vertex, girth, clique number, chromatic number, independence number, and domination number. In addition to these properties, we study dimensions of prime ideal graphs, including metric dimension, local metric dimension, and partition dimension; furthermore, we examined topological indices such as atom bond connectivity index, Balaban index, Szeged index, and edge-Szeged index.

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The matrix Jacobson graph of finite commutative rings

Cited by 2 publications

References 0 publications

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

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

On Properties of Prime Ideal Graphs of Commutative Rings

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