THE JACOBSON GRAPH OF COMMUTATIVE RINGS

DOI10.1142/S0219498812501794zbMath1262.05076MaRDI QIDQ4916168

A. Azimi, Ahmad Erfanian, Mohammad Farrokhi D. G.

Publication date: 19 April 2013

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

zbMATH Keywords

diameterindependence numberconnectivitydominating numberplanaritygirthclique numberperfectnesslocal ringJacobson graphvertex and edge chromatic number

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Planar graphs; geometric and topological aspects of graph theory (05C10) 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) Jacobson radical, quasimultiplication (16N20) Perfect graphs (05C17) Local rings and semilocal rings (13H99)

Related Items (14)

Classification of finite commutative rings with planar, toroidal, and projective line graphs associated with Jacobson graphs ⋮ The genus two class of graphs arising from rings ⋮ The matrix Jacobson graph of finite commutative rings ⋮ When is the Jacobson graph projective? ⋮ The proof of a conjecture in Jacobson graph of a commutative ring ⋮ Some new results on Jacobson graphs ⋮ Classification of the toroidal Jacobson graphs ⋮ Some results on the Jacobson graph of a commutative ring ⋮ Classification of rings with toroidal Jacobson graph ⋮ Chordality of graphs associated to commutative rings ⋮ Isomorphisms between Jacobson graphs ⋮ Computing Wiener and hyper-Wiener indices of zero-divisor graph of \(\mathbb{Z}_{g^3}\times\mathbb{Z}_{\mathfrak{I}_1\mathfrak{I}_2}\) ⋮ A survey on genus of selected graphs from commutative rings ⋮ On strong metric dimension of zero-divisor graphs of rings

Cites Work

• Unnamed Item
• The strong perfect graph theorem
• Coloring of commutative rings
• The zero-divisor graph of a commutative ring
• Beck's coloring of a commutative ring
• Rings of order \(p^5\). I: Nonlocal rings
• A note on graphical representation of rings
• Intersection graphs of ideals of rings

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