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Chromatic number of the zero-divisor graphs over modules

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초록

Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. The main purpose of this paper is to calculate the chromatic number of the zero-divisor graphs over modules.

Abstract

Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. The main purpose of this paper is to calculate the chromatic number of the zero-divisor graphs over modules.

참고문헌 (9)

  1. S. Akbari, "On zero-divisor graphs of nite rings", J. Algebra, 314(1), pp.168~184 (2007)
  2. D. F. Anderson, "The zero-divisor graph of a commutative ring", J. Algebra, 217(2), pp.434~447 (1999)
  3. I. Beck, "Coloring of commutative rings", J. Algebra, 116(1), pp.208~226 (1988)
  4. M. Behboodi, "Zero divisor graphs for modules over commutative rings", J. Commut. Al-gebra, 4(2), pp.175~197 (2012)
  5. 이상철, "Semiprime submodules of graded multiplication modules", 대한수학회지, 49(2), pp.435~447 (2012), 대한수학회
  6. 이상철, "ZERO-DIVISOR GRAPHS OF MULTIPLICATION MODULES", 호남수학학술지, 34(4), pp.571~584 (2012), 호남수학회[DOI]
  7. D. Lu and T. Wu, "On bipartite zero-divisor graphs", Discrete Math, 309(4), pp.755~762 (2009)
  8. SHARIEFUDDIN PIRZADA, "On graphs associated with modules over commutative rings", 대한수학회지, 53(5), pp.1167~1182 (2016), 대한수학회
  9. T. Wu, "On directed zero-divisor graphs of nite rings", Discrete Math, 296(1), pp.73~86 (2005)

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