Some properties of generalized comaximal graph of commutative ring

B Biswas, S Kar - Soft Computing, 2024 - Springer
In this paper, we extend our investigation about the generalized comaximal graph
introduced in Biswas et al.(Discrete Math Algorithms Appl 11 (1): 1950013, 2019a). The …

Computing degree based topological indices of algebraic hypergraphs

AS Alali, EÖ Sözen, C Abdioğlu, S Ali, E Eryaşar - Heliyon, 2024 - cell.com
Topological indices are numerical parameters that indicate the topology of graphs or
hypergraphs. A hypergraph H=\(V\(H\), E\(H\)\) consists of a vertex set V\(H\) and an edge set …

Embedding of prime ideal sum graph of a commutative ring on surfaces

P Mathil, B Baloda, J Kumar - arXiv preprint arXiv:2210.15335, 2022 - arxiv.org
Let $ R $ be a commutative ring with unity. The prime ideal sum graph $\text {PIS}(R) $ of the
ring $ R $ is the simple undirected graph whose vertex set is the set of all nonzero proper …

Upper ideal relation graphs associated to rings

B Baloda, J Kumar - Soft Computing, 2024 - Springer
Let R be a ring with unity. The upper ideal relation graph Γ U (R) of the ring R is a simple
undirected graph whose vertex set is the set of all non-unit elements of R and two distinct …

On the idempotent graph of a ring

P Mathil, B Baloda, J Kumar - arXiv preprint arXiv:2306.08327, 2023 - arxiv.org
Let $ R $ be a ring with unity. The\emph {idempotent graph} $ G_ {\text {Id}}(R) $ of a ring $
R $ is an undirected simple graph whose vertices are the set of all the elements of ring $ R …

Characterization of rings with planar, toroidal or projective planar prime ideal sum graphs

P Mathil, B Baloda, J Kumar… - … International Journal of …, 2024 - Taylor & Francis
Let R be a commutative ring with unity. The prime ideal sum graph PIS (R) of the ring R is
the simple undirected graph whose vertex set is the set of all nonzero proper ideals of R and …

Characterization of rings with genus two cozero-divisor graphs

P Mathil, B Baloda, J Kumar - arXiv preprint arXiv:2212.12900, 2022 - arxiv.org
Let $ R $ be a ring with unity. The cozero-divisor graph of a ring $ R $ is an undirected
simple graph whose vertices are the set of all non-zero and non-unit elements of $ R $ and …

Characterization of rings with genus two prime ideal sum graphs

P Mathil, J Kumar - arXiv preprint arXiv:2308.04048, 2023 - arxiv.org
Let $ R $ be a commutative ring with unity. The prime ideal sum graph of the ring $ R $ is a
simple undirected graph whose vertex set is the set of nonzero proper ideals of $ R $ and …

On the graph over commutative ring R

B Biswas, S Kar - ANNALI DELL'UNIVERSITA'DI FERRARA, 2024 - Springer
Let R be a commutative ring with identity 1. Then the graph of R, denoted by GP (R) which is
defined as the vertices are the elements of R and any two distinct elements a and b are …

[PDF][PDF] Independence and domination number of order two element graph over a group.

S Pradhan, S Kar, B Biswas - Discrete Mathematics, Algorithms & …, 2025 - researchgate.net
Let G be a group. Then the order two element graph of G is the simple undirected graph
whose vertex set consists of all elements of G and two distinct vertices u, v are adjacent if …