On a graph of monogenic semigroups

Das, Kinkar Ch.; Akgüneş, Nihat; Çevik, A. Sinan

doi:10.1186/1029-242x-2013-44

Cited by 24 publications

(39 citation statements)

References 15 publications

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“…The literature on zero-divisor graphs of semigroups discusses many classifications of semigroups, such as commutative semigroups and monogenic semigroups. The zero-divisor graphs of monogenic semigroups were studied by Das et al (2013). This particular work will continue this investigation.…”

Section: Introductionmentioning

confidence: 85%

“…In other words, the two vertices and in ( ) are adjacent when = 0, where ( ) is the set of zerodivisors. In Das et al (2013), the zero-divisor graph Γ( ) for a monogenic semigroup with {0} is defined as an undirected graph whose nonzero vertices i , j ∈ are adjacent if they satisfy the following: i . j = 0 only if + > where 1 ≤ , ≤ .…”

Section: Introductionmentioning

confidence: 99%

“…j = 0 only if + > where 1 ≤ , ≤ . In this work, we add one more condition to the graph obtained in Das et al (2013) to obtain a new zero-divisors monogenic semigroup graph, and its characteristics will be studied.…”

Section: Introductionmentioning

confidence: 99%

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The Zero-Divisor Graphs of Variation Monogenic Semigroups

Subaiei¹,

Akwu²

2020

SJKFU

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The undirected graph Γ() is the zero-divisor graph of the monogenic semigroup S M with zero. The non-zero vertices i and j of this graph are adjacent whenever + > and gcd(,) = 1, where is the order of Γ(). In this work, we consider some properties of the graph Γ(), such as the diameter, girth, chromatic number and clique. In addition, we show that Γ() is a perfect, well-covered and coprime graph.

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Section: Introductionmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

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The Zero-Divisor Graphs of Variation Monogenic Semigroups

Subaiei¹,

Akwu²

2020

SJKFU

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“…In particular, they proved that the zero-divisor graph of a commutative semigroup with zero is connected. Since then, the zero-divisor graphs of some special classes of commutative semigroups with zero have been researched (see [4,17] ). For non-commutative rings, a directed zero-divisor graph and some undirected zero-divisor graphs were defined by Redmond in [14].…”

Section: Introductionmentioning

confidence: 99%

Zero-divisor graphs of Catalan monoid

Toker

2021

Hacettepe Journal of Mathematics and Statistics

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Let C n be the Catalan monoid on X n = {1,. .. , n} under its natural order. In this paper, we describe the sets of left zero-divisors, right zero-divisors and two sided zero-divisors of C n ; and their numbers. For n ≥ 4, we define an undirected graph Γ(C n) associated with C n whose vertices are the two sided zero-divisors of C n excluding the zero element θ of C n with distinct two vertices α and β joined by an edge in case αβ = θ = βα. Then we first prove that Γ(C n) is a connected graph, and then we find the diameter, radius, girth, domination number, clique number and chromatic numbers and the degrees of all vertices of Γ(C n). Moreover, we prove that Γ(C n) is a chordal graph, and so a perfect graph.

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“…

AbstractIn Das et al (2013), it has been defined a new algebraic graph on monogenic semigroups. Our main scope in this study, is to extend this study over the special algebraic graphs to the strong product.

…”

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confidence: 99%

Some graph parameters on the strong product of monogenic semigroup graphs

Akgüneş¹

2018

Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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In Das et al. (2013), it has been defined a new algebraic graph on monogenic semigroups. Our main scope in this study, is to extend this study over the special algebraic graphs to the strong product. In detail, we will determinate some important graph parameters (diameter, girth, radius, maximum degree, minimum degree, chromatic number, clique number and domination number) for the strong product of any two monogenic semigroup graphs.

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On a graph of monogenic semigroups

Abstract: Let us consider the finite monogenic semigroup S M

Cited by 24 publications

References 15 publications

The Zero-Divisor Graphs of Variation Monogenic Semigroups

The Zero-Divisor Graphs of Variation Monogenic Semigroups

Zero-divisor graphs of Catalan monoid

Some graph parameters on the strong product of monogenic semigroup graphs

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