1. Some properties of generalized comaximal graph of commutative ring.
- Author
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Biswas, B. and Kar, S.
- Subjects
- *
FINITE rings , *LOCAL rings (Algebra) , *COMMUTATIVE rings , *UNDIRECTED graphs , *PLANAR graphs , *MATHEMATICS , *MATRIX rings , *HAMILTONIAN graph theory - 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]
- Published
- 2024
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