On the Cayley Graph of a Commutative Ring with Respect to its Zero-divisors

DOI10.1080/00927872.2015.1027359zbMath1341.05114arXiv1305.0601OpenAlexW1546434947MaRDI QIDQ2810614

Saieed Akbari, Ghodratollah Aalipour

Publication date: 3 June 2016

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.0601

zbMATH Keywords

Cayley graphchromatic numberclique numberminimal prime idealzero-dimensional ringzero-divisor

Mathematics Subject Classification ID

Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Coloring of graphs and hypergraphs (05C15) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69) Connectivity (05C40) Eulerian and Hamiltonian graphs (05C45)

Related Items (4)

Comparison of graphs associated to a commutative Artinian ring ⋮ UNIT AND UNITARY CAYLEY GRAPHS FOR THE RING OF EISENSTEIN INTEGERS MODULO \(n\) ⋮ Reduction graph and its application on algebraic graphs ⋮ On coupon coloring of Cayley graphs

Cites Work

• Energy of unitary Cayley graphs and gcd-graphs
• The energy of unitary Cayley graphs
• The total graph and regular graph of a commutative ring
• The total graph of a commutative ring
• Connectivity of Cartesian products of graphs
• Hamiltonian circuits in Cayley graphs
• The zero-divisor graph of a commutative ring
• On the Total Graph of a Finite Commutative Ring
• A note on principal ideals and J-classes in the direct product of two semigroups
• Some Properties of a Cayley Graph of a Commutative Ring
• Connectivity of transitive graphs
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