Zero-divisor graphs of genus one

DOI10.1016/j.jalgebra.2006.01.057zbMath1106.13029OpenAlexW2047344301MaRDI QIDQ855329

Hsin-Ju Wang

Publication date: 7 December 2006

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2006.01.057

Mathematics Subject Classification ID

Structure of finite commutative rings (13M05)

Related Items (46)

Local Rings with Genus Two Zero Divisor Graph ⋮ RINGS WHOSE ANNIHILATING-IDEAL GRAPHS HAVE POSITIVE GENUS ⋮ Unnamed Item ⋮ A class of zero divisor rings in which every graph is precisely the union of a complete graph and a complete bipartite graph ⋮ On the planarity of the \(k\)-zero-divisor hypergraphs ⋮ The genus two class of graphs arising from rings ⋮ Finite commutative rings whose unitary Cayley graphs have positive genus ⋮ On the planarity, genus and crosscap of new extension of zero-divisor graph of commutative rings ⋮ Finite commutative ring with genus two essential graph ⋮ Projective total graphs of commutative rings ⋮ Planar, outerplanar, and toroidal graphs of the generalized zero-divisor graph of commutative rings ⋮ Classification of non-local rings with projective 3-zero-divisor hypergraph ⋮ The embedding of line graphs associated to the zero-divisor graphs of commutative rings ⋮ On the genus of extended zero-divisor graph of commutative rings ⋮ On the genus of dot product graph of a commutative ring ⋮ Crosscap of the ideal based zero-divisor graph ⋮ Toroidal zero-divisor graphs of decomposable commutative rings without identity ⋮ Classification of nonlocal rings with genus one 3-zero-divisor hypergraphs ⋮ On zero-divisor graphs of commutative rings without identity ⋮ Classification of rings with projective zero-divisor graphs ⋮ Finite groups whose noncyclic graphs have positive genus ⋮ On the genus of the zero-divisor graph of \(\mathbb Z_n\) ⋮ On the genus of generalized unit and unitary Cayley graphs of a commutative ring ⋮ The genus of graphs associated with vector spaces ⋮ Classification of rings with toroidal and projective coannihilator graph ⋮ Power graphs of (non)orientable genus two ⋮ On the Annihilator Graph of a Commutative Ring ⋮ On the Genus of the Total Graph of a Commutative Ring ⋮ A survey on the Intersection graphs of ideals of rings ⋮ Graphs associated to co-maximal ideals of commutative rings ⋮ The Zero Divisor Graphs of Commutative Local Rings of Orderp⁴andp⁵ ⋮ A kind of intersection graph of vector space ⋮ Rings whose total graphs have genus at most one ⋮ ON THE GENUS OF THE INTERSECTION GRAPH OF IDEALS OF A COMMUTATIVE RING ⋮ Classification of rings with toroidal Jacobson graph ⋮ Toroidality of intersection graphs of ideals of commutative rings ⋮ Classification of Rings with Genus One Zero-Divisor Graphs ⋮ Rings whose zero-divisor graphs have positive genus ⋮ Classification of Finite Groups with Toroidal or Projective-Planar Permutability Graphs ⋮ Classification of rings with crosscap two class of graphs ⋮ Classification of non-local rings with genus two zero-divisor graphs ⋮ Finite commutative rings with higher genus unit graphs ⋮ On the Dot Product Graph of a Commutative Ring ⋮ Commutative Rings Whose Zero-Divisor Graphs Have Positive Genus ⋮ A survey on genus of selected graphs from commutative rings ⋮ A note on subspace sum graph of vector spaces

Cites Work

• Unnamed Item
• The zero-divisor graph of a commutative ring
• When a zero-divisor graph is planar or a complete \(r\)-partite graph
• On the zero-divisor graph of a commutative ring
• CYCLES AND SYMMETRIES OF ZERO-DIVISORS
• SOLUTION OF THE HEAWOOD MAP-COLORING PROBLEM

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