Some remarks on the Roman domination number of the complement of the zero-divisor graph of a commutative ring

	Some remarks on the Roman domination number of the complement of the zero-divisor graph of a commutative ring
Communications in Combinatorics and Optimization
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 06 شهریور 1405
نوع مقاله: Original paper
شناسه دیجیتال (DOI): 10.22049/cco.2026.31138.2755
نویسنده
S. Visweswaran^*
Saurashtra University
چکیده
The rings considered in this paper are commutative with identity that admit at least one nonzero zero-divisor. Let R be a ring. Let Z(R) denote the set of all zero-divisors of R. Let Z(R)* denote the set of all nonzero zero-divisors of R. Recall that the zero-divisor graph of R, is an undirected graph whose vertex set is Z(R)* and distinct vertices x and y are adjacent if and only if xy = 0. This paper aims to determine the Roman domination number of the complement of the zero-divisor graph of R with the assumption that its domination number is finite.
کلیدواژه‌ها
Reduced ring؛ domination number؛ Roman domination number

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