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Some properties of generalized comaximal graph of commutative ring.

Authors :
Biswas, B.
Kar, S.
Source :
Soft Computing - A Fusion of Foundations, Methodologies & Applications; Mar2024, Vol. 28 Issue 5, p3783-3791, 9p
Publication Year :
2024

Abstract

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 generalized comaximal graph is defined as follows: given a finite commutative ring R, the generalized comaximal graph G(R) is an undirected graph with its vertex set comprising elements of R and two distinct vertices u, v are adjacent if and only if there exists a non-zero idempotent e ∈ R such that u R + v R = e R . In this study, we focus on identifying the rings R for which the graph G(R) exhibits planarity. Moreover, we provide a characterization of the class of ring for which G(R) is toroidal, denoted by γ (G (R)) = 1 . Furthermore, we also evaluate the energy of the graph G(R). Finally, we demonstrate that the graph G(R) is always Hamiltonian for any finite commutative ring R. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
14327643
Volume :
28
Issue :
5
Database :
Complementary Index
Journal :
Soft Computing - A Fusion of Foundations, Methodologies & Applications
Publication Type :
Academic Journal
Accession number :
175389982
Full Text :
https://doi.org/10.1007/s00500-023-09572-0