Total coloring of graphs associated with algebraic structures and ordered structures Total coloring of graphs associated with algebraic structures and ordered structures

In this paper, we prove that the zero-divisor graphs of finite posets and the complement of zero-divisor graphs of finite 0-distributive posets satisfy the Total Coloring Conjecture. These results are applied to zero-divisor graphs of finite reduced commutative rings, comaximal ideal graphs, (co-) a...

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Bibliographic Details
Published inIndian journal of pure and applied mathematics Vol. 56; no. 2; pp. 535 - 544
Main Authors Khandekar, Nilesh, Joshi, Vinayak
Format Journal Article
LanguageEnglish
Published New Delhi Indian National Science Academy 01.06.2025
Springer Nature B.V
Subjects
Applications of Mathematics
Coloring
Commutativity
Graphs
Mathematics
Mathematics and Statistics
Numerical Analysis
Original Research
Rings (mathematics)
Coloring of a graph
13A70
Zero-divisor graphs
Pseudocomplemented poset
Total Coloring Conjecture
Direct product of posets
Comaximal ideal graph
Reduced ring
05C15
06A07
Online AccessGet full text
ISSN0019-5588
0975-7465
DOI10.1007/s13226-023-00500-4

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Summary:In this paper, we prove that the zero-divisor graphs of finite posets and the complement of zero-divisor graphs of finite 0-distributive posets satisfy the Total Coloring Conjecture. These results are applied to zero-divisor graphs of finite reduced commutative rings, comaximal ideal graphs, (co-) annihilating ideal graphs of commutative rings with finitely many ideals and intersection graphs of Artinian principal ideal rings.
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ISSN:0019-5588
0975-7465
DOI:10.1007/s13226-023-00500-4