General form of domination polynomial for two types of graphs associated to dihedral groups
A domination polynomial is a type of graph polynomial in which its coefficients represent the number of dominating sets in the graph. There are many researches being done on the domination polynomial of some common types of graphs but not yet for graphs associated to finite groups. Two types of grap...
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Penerbit UTM Press
2019
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| Online Access: | http://eprints.utm.my/84880/1/NorHanizaSarmin2019_GeneralFormofDominationPolynomial.pdf |
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| author | Najmuddin, Nabilah Sarmin, Nor Haniza Erfanian, Ahmad |
| author_facet | Najmuddin, Nabilah Sarmin, Nor Haniza Erfanian, Ahmad |
| author_sort | Najmuddin, Nabilah |
| collection | ePrints |
| description | A domination polynomial is a type of graph polynomial in which its coefficients represent the number of dominating sets in the graph. There are many researches being done on the domination polynomial of some common types of graphs but not yet for graphs associated to finite groups. Two types of graphs associated to finite groups are the conjugate graph and the conjugacy class graph. A graph of a group G is called a conjugate graph if the vertices are non-central elements of G and two distinct vertices are adjacent if they are conjugate to each other. Meanwhile, a conjugacy class graph of a group G is a graph in which its vertices are the non-central conjugacy classes of G and two distinct vertices are connected if and only if their class cardinalities are not coprime. The conjugate and conjugacy class graph of dihedral groups can be expressed generally as a union of complete graphs on some vertices. In this paper, the domination polynomials are computed for the conjugate and conjugacy class graphs of the dihedral groups. |
| first_indexed | 2024-03-05T20:34:10Z |
| format | Article |
| id | utm.eprints-84880 |
| institution | Universiti Teknologi Malaysia - ePrints |
| language | English |
| last_indexed | 2024-03-05T20:34:10Z |
| publishDate | 2019 |
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| spelling | utm.eprints-848802020-02-29T12:39:55Z http://eprints.utm.my/84880/ General form of domination polynomial for two types of graphs associated to dihedral groups Najmuddin, Nabilah Sarmin, Nor Haniza Erfanian, Ahmad QA Mathematics A domination polynomial is a type of graph polynomial in which its coefficients represent the number of dominating sets in the graph. There are many researches being done on the domination polynomial of some common types of graphs but not yet for graphs associated to finite groups. Two types of graphs associated to finite groups are the conjugate graph and the conjugacy class graph. A graph of a group G is called a conjugate graph if the vertices are non-central elements of G and two distinct vertices are adjacent if they are conjugate to each other. Meanwhile, a conjugacy class graph of a group G is a graph in which its vertices are the non-central conjugacy classes of G and two distinct vertices are connected if and only if their class cardinalities are not coprime. The conjugate and conjugacy class graph of dihedral groups can be expressed generally as a union of complete graphs on some vertices. In this paper, the domination polynomials are computed for the conjugate and conjugacy class graphs of the dihedral groups. Penerbit UTM Press 2019 Article PeerReviewed application/pdf en http://eprints.utm.my/84880/1/NorHanizaSarmin2019_GeneralFormofDominationPolynomial.pdf Najmuddin, Nabilah and Sarmin, Nor Haniza and Erfanian, Ahmad (2019) General form of domination polynomial for two types of graphs associated to dihedral groups. MATEMATIKA, 35 (Aug). pp. 149-155. ISSN 0127-9602 https://dx.doi.org/10.11113/matematika.v35.n2.1106 DOI:10.11113/matematika.v35.n2.1106 |
| spellingShingle | QA Mathematics Najmuddin, Nabilah Sarmin, Nor Haniza Erfanian, Ahmad General form of domination polynomial for two types of graphs associated to dihedral groups |
| title | General form of domination polynomial for two types of graphs associated to dihedral groups |
| title_full | General form of domination polynomial for two types of graphs associated to dihedral groups |
| title_fullStr | General form of domination polynomial for two types of graphs associated to dihedral groups |
| title_full_unstemmed | General form of domination polynomial for two types of graphs associated to dihedral groups |
| title_short | General form of domination polynomial for two types of graphs associated to dihedral groups |
| title_sort | general form of domination polynomial for two types of graphs associated to dihedral groups |
| topic | QA Mathematics |
| url | http://eprints.utm.my/84880/1/NorHanizaSarmin2019_GeneralFormofDominationPolynomial.pdf |
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