Metric and Strong Metric Dimension in Cozero-Divisor Graphs

Nikandish, Reza; Nikmehr, M. J.; Bakhtyiari, M.

doi:10.1007/s00009-021-01772-y

Cited by 10 publications

(4 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Wheel related [120] Cozero-divisor graphs [148] Generalized Petersen [118] graphs graphs Zero-divisor [24] Cactus graphs [122] Annihilator graphs [50] graphs of rings of commutative rings Table 2: Some other studies on the strong metric dimension of graphs.…”

Section: Graph Familymentioning

confidence: 99%

Metric dimension related parameters in graphs: A survey on combinatorial, computational and applied results

Kuziak,

Yero

2021

Preprint

View full text Add to dashboard Cite

show abstract

Section: Graph Familymentioning

confidence: 99%

Metric dimension related parameters in graphs: A survey on combinatorial, computational and applied results

Kuziak,

Yero

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Akbari et al [5], studied the cozero-divisor graph associated with the ring R[x]. Some of the work associated with the cozero-divisor graph on the rings can be found in [3,4,6,7,11,12]. In this paper, we deal with the Laplacian spectrum of cozero-divisor graph on the ring Z n .…”

Section: Introductionmentioning

confidence: 99%

On the cozero-divisor graphs assosciated to rings

Praveen¹,

Kumar²

2022

Preprint

View full text Add to dashboard Cite

Let R be a ring with unity. The cozero-divisor graph of a ring R, denoted by Γ (R), is an undirected simple graph whose vertices are the set of all non-zero and non-unit elements of R, and two distinct vertices x and y are adjacent if and only if x / ∈ Ry and y / ∈ Rx. In this paper, we study the Laplacian spectrum of Γ (Zn). We show that the graph Γ (Zpq) is Laplacian integral. Further, we obtain the Laplacian spectrum Γ (Zn) for n = p n 1 q n 2 ,where n 1 , n 2 ∈ N and p, q are distinct primes.

show abstract

“…At the final part of this paper, we provide a SageMath code to compute the Wiener index of the cozero-divisor graph of these class of rings including the ring Zn of integers modulo n. et al [5] studied the cozero-divisor graph associated to the polynomial ring and the ring of power series. Some of the work associated with the cozero-divisor graphs of rings can be found in [3,4,7,11,23,24,25].Over the recent years, the Wiener index of certain graphs associated with rings have been studied by various authors. The Wiener index of the zero divisor graph of the ring Z n of integers modulo n has been studied in [10].…”

mentioning

confidence: 99%

mentioning

confidence: 99%

Wiener index of the Cozero-divisor graph of a finite commutative ring

Baloda¹,

Praveen²,

Kumar³

et al. 2022

Preprint

View full text Add to dashboard Cite

Let R be a ring with unity. The cozero-divisor graph of a ring R, denoted by Γ ′ (R), is an undirected simple graph whose vertices are the set of all non-zero and non-unit elements of R, and two distinct vertices x and y are adjacent if and only if x / ∈ Ry and y / ∈ Rx. In this article, we extend some of the results of [24] to an arbitrary ring. In this connection, we derive a closed-form formula of the Wiener index of the cozero-divisor graph of a finite commutative ring R. As applications, we compute the Wiener index of Γ ′ (R), when either R is the product of ring of integers modulo n or a reduced ring. At the final part of this paper, we provide a SageMath code to compute the Wiener index of the cozero-divisor graph of these class of rings including the ring Zn of integers modulo n. et al. [5] studied the cozero-divisor graph associated to the polynomial ring and the ring of power series. Some of the work associated with the cozero-divisor graphs of rings can be found in [3,4,7,11,23,24,25].Over the recent years, the Wiener index of certain graphs associated with rings have been studied by various authors. The Wiener index of the zero divisor graph of the ring Z n of integers modulo n has been studied in [10]. Recently, Selvakumar et al. [28] calculated the Wiener index of the zero divisor graph for a finite commutative ring with unity. The Wiener index of the cozero-divisor graph of the ring Z n has been obtained in [24]. In order to extend the results of [24] to an arbitrary ring, we study the Wiener index of the cozero-divisor graph of a finite commutative 2020 Mathematics Subject Classification. 05C25, 05C50.

show abstract

Metric and Strong Metric Dimension in Cozero-Divisor Graphs

Cited by 10 publications

References 16 publications

Metric dimension related parameters in graphs: A survey on combinatorial, computational and applied results

Metric dimension related parameters in graphs: A survey on combinatorial, computational and applied results

On the cozero-divisor graphs assosciated to rings

Wiener index of the Cozero-divisor graph of a finite commutative ring

Contact Info

Product

Resources

About