On the annihilator graphs of partial transformation semigroups
Let [Formula: see text] and [Formula: see text] be a partial transformation semigroup on [Formula: see text] Obviously, the empty set [Formula: see text] is a zero element of [Formula: see text] and denoted by 0. Let [Formula: see text] An element [Formula: see text] is a zero divisor of [Formula: s...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2024-12-01
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| Series: | Arab Journal of Basic and Applied Sciences |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/25765299.2024.2423464 |
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| Summary: | Let [Formula: see text] and [Formula: see text] be a partial transformation semigroup on [Formula: see text] Obviously, the empty set [Formula: see text] is a zero element of [Formula: see text] and denoted by 0. Let [Formula: see text] An element [Formula: see text] is a zero divisor of [Formula: see text] if there exists [Formula: see text] such that [Formula: see text] The set [Formula: see text] is called the annihilator of [Formula: see text] in [Formula: see text] It is clear that [Formula: see text] for all [Formula: see text] Let [Formula: see text] be the set of all zero divisors of [Formula: see text] and [Formula: see text] Generally, if [Formula: see text] then there exists [Formula: see text] in which [Formula: see text] In this paper, we construct the annihilator graph [Formula: see text] of [Formula: see text] which is an undirected simple graph with vertex set [Formula: see text] and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text] Furthermore, we prove some basic structural properties of [Formula: see text] and determine invariants for [Formula: see text] such as the diameter, girth, clique, domination number, and independence number. |
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| ISSN: | 2576-5299 |