On Beck’ s Coloring for Measurable Functions

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ASSARI A.; RAHIMI M.

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Paper Information

Journal: IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS Year:2021 | Volume:16 | Issue:2 Page(s): 1-10

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Title

On Beck’ s Coloring for Measurable Functions

Author(s)

ASSARI A. | RAHIMI M. | Issue Writer Certificate

Keywords

Clique number

Coloring

Domination number

Measurable function

Zero divisor graph

Abstract

We study Beck-like coloring of measurable functions on a measure space Ω taking values in a measurable semigroup Δ . To any measure space Ω and any measurable semigroup Δ , we assign a graph (called a zero-divisor graph) whose vertices are labeled by the classes of measurable functions defined on Ω and having values in Δ , with two vertices f and g adjacent if f g = 0 a. e. . We show that, if Ω is atomic, then not only the Beck’ s conjecture holds but also the domination number coincides to the clique number and chromatic number as well. We also determine some other graph properties of such a graph.

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APA: Copy

ASSARI, A., & RAHIMI, M.. (2021). On Beck’ s Coloring for Measurable Functions. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), 16(2), 1-10. SID. https://sid.ir/paper/689656/en

Vancouver: Copy

ASSARI A., RAHIMI M.. On Beck’ s Coloring for Measurable Functions. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI)[Internet]. 2021;16(2):1-10. Available from: https://sid.ir/paper/689656/en

IEEE: Copy

A. ASSARI, and M. RAHIMI, “On Beck’ s Coloring for Measurable Functions,” IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), vol. 16, no. 2, pp. 1–10, 2021, [Online]. Available: https://sid.ir/paper/689656/en

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