Comments on the Clique Number of Zero‐Divisor Graphs of Zn

Tian, Yanzhao; Li, Lixiang

doi:10.1155/2022/6591317

Cited by 4 publications

(2 citation statements)

References 27 publications

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“…Moreover, we choose Python for computational algebra due to its versatility, ease of learning, strong community support, seamless integration with other tools, and the availability of powerful numerical computing libraries like NumPy and SciPy, as well as graph plotting libraries like Matplotlib and NetworkX. In the concept of a graph of a ring, several researchers used the Python algorithm as in [12], [13], and [14]. In this paper, we discuss the algorithm to construct 𝑇𝑍𝛤(ℤ 𝑛 ) using Python.…”

Section: Introductionmentioning

confidence: 99%

CONSTRUCT THE TRIPLE ZERO GRAPH OF RING Z_n USING PYTHON

Wulandari,

Kurniawan,

Kurdhi

2024

BAREKENG: J. Math. & App.

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Let be a commutative ring with nonzero identity and there exists such that , , , denotes the set of all triple zero elements of . The triple zero graph of , denoted by , is an undirected graph with vertex set where two distinct vertices and are adjacent if and only if , and there exists a nonzero element of such that , , and . Python is a programming language with simple and easy-to-learn code that can be used to solve problems in algebra and graphs. In this paper, we construct the triple zero graph of ring using Python. Based on the output of the program, several properties of are obtained, such as if and , then is a planar graph, if with is prime numbers, then is a complete graph , and if with is prime numbers and , then is a connected graph.

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Section: Introductionmentioning

confidence: 99%

CONSTRUCT THE TRIPLE ZERO GRAPH OF RING Z_n USING PYTHON

Wulandari,

Kurniawan,

Kurdhi

2024

BAREKENG: J. Math. & App.

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“…Python was created by Guido van Rossum in the late 1980s and early 1990s at the National Research Institute for Mathematics and Computer Science in Netherlands (Saabith et al, 2019). In the graphic concept of ring, several researchers have used python algorithms such as in (Tapanyo et al, 2022), (Kansal et al, 2022), (Hartati & Kurniawan, 2023), and (Tian & Li, 2022). In previous research, no algorithm was given to construct the total graph.…”

mentioning

confidence: 99%

Algorithm for Constructing Total Graph of Commutative Ring

Meinawati,

Kurniawan,

Kurdhi

2024

JTAM

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Let R be a commutative ring. The total graph of R, denoted by TΓ(R) is a graph whose vertices are all elements of the ring R and every i,j∈R with i≠j, then i and j vertices are connected by edges if and only if i+j∈Z(R), where Z(R) is the set of zero-divisors in R with 0∈Z(R). Python programming is code that is easy to learn, read, understand, and helpful in explaining problems regarding graphs and algebra. In this paper, we determine an algorithm to construct the total graph of ring Z_n using Python. The research methods in this paper is a literature studies. The results generated by the algorithm can be utilized to observe the characteristic patterns displayed by the graph. Based on the algorithm’s constructed graph pattern, several properties of TΓ(Z_n ) can be inferred. For instance, if n is a prime number, then TΓ(Z_n ) is a disconnected graph. On the other hand, if n is a prime number and n≥3, then TΓ(Z_2n ) and TΓ(Z_4n ) is a connected graph, regular graph, Hamiltonian graph, and has a girth gr(TΓ(〖Z〗_n ))=3. In this paper we creating an algorithm to construct total graphs from commutative rings streamlines the construction process, enhances accessibility and utilization of total graphs, and supports parameter variation exploration and application in problem-solving.

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