Year: 2025
Type: article
Abstract: Let S=C×⋯×C (k times) and 1≤k<∞ be an integer, where C is a commutative ring with unity 1≠0. In this paper, we classify the rings S such that the extended total dot product graph TD¯¯¯¯¯¯¯¯(S) and the extended zero-divisor dot product graph ZD¯¯¯¯¯¯¯¯(S) have genus one and two. Furthermore, we characterize S such that the total dot product graph TD(S) and the zero-divisor dot product graph ZD(S) have crosscap one and two.
Authors: A. Ali, N. H. Sarmin, B. Ahmad
Institutions: Aligarh Muslim University, University of Technology Malaysia
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4414148126