Total graphs of Polynomial Rings and Rings of fractions
سال
: 2013
چکیده: Let R be a commutative ring. The total graph of R, denoted by T(Γ(R)), is a graph
with all elements of R as vertices, and two distinct vertices x, y ∈ R are adjacent if and
only if x + y ∈ Z(R), where Z(R) denotes the set of zero-divisors of R. In this paper,
we examine the preservation of the diameter, girth and completeness of T(Γ(R)) under
extension to polynomial rings and rings of fractions. We also study the chromatic index,
clique number and independence number of T(Γ(R)).
with all elements of R as vertices, and two distinct vertices x, y ∈ R are adjacent if and
only if x + y ∈ Z(R), where Z(R) denotes the set of zero-divisors of R. In this paper,
we examine the preservation of the diameter, girth and completeness of T(Γ(R)) under
extension to polynomial rings and rings of fractions. We also study the chromatic index,
clique number and independence number of T(Γ(R)).
کلیدواژه(گان): Total graph,diameter,girth,polynomial rings,rings of fractions,chromatic index,clique number
کالکشن
:
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آمار بازدید
Total graphs of Polynomial Rings and Rings of fractions
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| contributor author | مژگان افخمی گلی | en |
| contributor author | کاظم خشیارمنش | en |
| contributor author | Kazem Khashyarmanesh | fa |
| date accessioned | 2020-06-06T13:16:54Z | |
| date available | 2020-06-06T13:16:54Z | |
| date issued | 2013 | |
| identifier uri | https://libsearch.um.ac.ir:443/fum/handle/fum/3348843 | |
| description abstract | Let R be a commutative ring. The total graph of R, denoted by T(Γ(R)), is a graph with all elements of R as vertices, and two distinct vertices x, y ∈ R are adjacent if and only if x + y ∈ Z(R), where Z(R) denotes the set of zero-divisors of R. In this paper, we examine the preservation of the diameter, girth and completeness of T(Γ(R)) under extension to polynomial rings and rings of fractions. We also study the chromatic index, clique number and independence number of T(Γ(R)). | en |
| language | English | |
| title | Total graphs of Polynomial Rings and Rings of fractions | en |
| type | Journal Paper | |
| contenttype | External Fulltext | |
| subject keywords | Total graph | en |
| subject keywords | diameter | en |
| subject keywords | girth | en |
| subject keywords | polynomial rings | en |
| subject keywords | rings of fractions | en |
| subject keywords | chromatic index | en |
| subject keywords | clique number | en |
| journal title | Discrete Mathematics, Algorithms and Applications | fa |
| pages | 135003501-135003512 | |
| journal volume | 5 | |
| journal issue | 4 | |
| identifier link | https://profdoc.um.ac.ir/paper-abstract-1039762.html | |
| identifier articleid | 1039762 |