When a total graph associated with a commutative ring is perfect?

DOI10.2298/PIM2021085JzbMath1471.13006MaRDI QIDQ4985678

Reza Nikandish, Mitra Jalali, Abolfazl Tehranian

Publication date: 24 April 2021

Published in: Publications de l'Institut Math?matique (Belgrade) (Search for Journal in Brave)

zbMATH Keywords

chromatic numberclique numberperfect graphtotal graph

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Ideals and multiplicative ideal theory in commutative rings (13A15) Graph theory (05C99) General commutative ring theory and combinatorics (zero-divisor graphs, annihilating-ideal graphs, etc.) (13A70)

Cites Work

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• Rings whose total graphs have genus at most one
• The clique numbers of regular graphs of matrix algebras are finite
• The total graph and regular graph of a commutative ring
• The total graph of a commutative ring
• Properties of rings with a finite number of zero divisors
• Balanced signed total graphs of commutative rings
• On the Total Graph and Its Complement of a Commutative Ring
• On the Total Graph of a Finite Commutative Ring
• On the Genus of the Total Graph of a Commutative Ring
• THE INTERSECTION GRAPH OF GAMMA SETS IN THE TOTAL GRAPH OF A COMMUTATIVE RING-II
• On the radius and the relation between the total graph of a commutative ring and its extensions
• The Total Graphs of Finite Rings

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