A large class of graphs with a small subclass of Cohen–Macaulay members

DOI10.1080/00927872.2022.2081333zbMath1495.13014OpenAlexW4286630373MaRDI QIDQ5038095

M. R. Pournaki, T. Ashitha, T. Asir

Publication date: 29 September 2022

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

Full work available at URL: https://doi.org/10.1080/00927872.2022.2081333

zbMATH Keywords

unit graphwell-covered graphfinite commutative ringCohen-Macaulay graphGorenstein graph

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Structural characterization of families of graphs (05C75) Combinatorial aspects of simplicial complexes (05E45) Combinatorial aspects of commutative algebra (05E40) General commutative ring theory and combinatorics (zero-divisor graphs, annihilating-ideal graphs, etc.) (13A70)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On CIS circulants
• Nonplanarity of unit graphs and classification of the toroidal ones
• Well-covered circulant graphs
• Necessary and sufficient conditions for unit graphs to be Hamiltonian
• Independence polynomials of circulants with an application to music
• On the ideal theory of graphs
• Cohen-Macaulay graphs
• Combinatorics and commutative algebra.
• Cohen-Macaulayness of two classes of circulant graphs
• Cohen-Macaulayness of a class of graphs versus the class of their complements
• Cohen--Macaulay chordal graphs
• Distributive lattices, bipartite graphs and Alexander duality
• Unit Graphs Associated with Rings
• Monomial Ideals
• WEAKLY PERFECT GRAPHS ARISING FROM RINGS
• Monomial Algebras
• Boolean graphs are Cohen–Macaulay
• Cohen–Macaulay Circulant Graphs
• Independence Complexes of Well-Covered Circulant Graphs