Total coloring of graphs associated with algebraic structures and ordered structures

Nilesh Khandekar () and Vinayak Joshi ()
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Nilesh Khandekar: Savitribai Phule Pune University
Vinayak Joshi: Savitribai Phule Pune University

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 2, 535-544

Abstract: Abstract 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.

Keywords: Zero-divisor graphs; Coloring of a graph; Total Coloring Conjecture; Comaximal ideal graph; Pseudocomplemented poset; Direct product of posets; Reduced ring; 05C15; 06A07; 13A70 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-023-00500-4

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