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In this paper, we introduce the concept of the associate class graph of zero-divisors of a commutative ring [Formula: see text], denoted by [Formula: see text]. Some properties of [Formula:… Click to show full abstract
In this paper, we introduce the concept of the associate class graph of zero-divisors of a commutative ring [Formula: see text], denoted by [Formula: see text]. Some properties of [Formula: see text], including the diameter, the connectivity and the girth are investigated. Utilizing this graph, we present a new class of counterexamples of Beck’s conjecture on the chromatic number of the zero-divisor graph of a commutative ring.
Keywords:
class graph;
associate class;
graph zero;
graph;
commutative ring
Journal Title: Journal of Algebra and Its Applications
Year Published: 2019
Link to full text (if available)
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Journal Title: Journal of Algebra and Its Applications
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!