Domination polynomial of clique cover product of graphs
Let \(G\) be a simple graph of order \(n\). We prove that the dominationpolynomial of the clique cover product \(G^\mathcal{C} \star H^{V(H)}\) is\[ D(G^\mathcal{C} \star H,x)=\prod_{i=1}^k\Big [\big((1+x)^{n_i}-1\big)(1+x)^{|V(H)|}+D(H,x)\Big],\]where each clique \(C_i \in \mathcal{C}\) has \(n_i\)...
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| Дата: | 2020 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2020
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/401 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543257823019008 |
|---|---|
| author | Jahari, Somayeh Alikhani, Saeid |
| author_facet | Jahari, Somayeh Alikhani, Saeid |
| author_sort | Jahari, Somayeh |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2020-02-10T19:12:26Z |
| description | Let \(G\) be a simple graph of order \(n\). We prove that the dominationpolynomial of the clique cover product \(G^\mathcal{C} \star H^{V(H)}\) is\[ D(G^\mathcal{C} \star H,x)=\prod_{i=1}^k\Big [\big((1+x)^{n_i}-1\big)(1+x)^{|V(H)|}+D(H,x)\Big],\]where each clique \(C_i \in \mathcal{C}\) has \(n_i\) vertices. As anapplication, we study the \(\mathcal{D}\)-equivalence classes of somefamilies of graphs and, in particular, describe completely the\(\mathcal{D}\)-equivalence classes of friendship graphs constructed bycoalescing \(n\) copies of a cycle graph of length 3 with a common vertex. |
| first_indexed | 2025-12-02T15:31:35Z |
| format | Article |
| id | admjournalluguniveduua-article-401 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:31:35Z |
| publishDate | 2020 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-4012020-02-10T19:12:26Z Domination polynomial of clique cover product of graphs Jahari, Somayeh Alikhani, Saeid domination polynomial, \(\mathcal{D}\)-equivalence class, clique cover, friendship graphs 05C60, 05C69 Let \(G\) be a simple graph of order \(n\). We prove that the dominationpolynomial of the clique cover product \(G^\mathcal{C} \star H^{V(H)}\) is\[ D(G^\mathcal{C} \star H,x)=\prod_{i=1}^k\Big [\big((1+x)^{n_i}-1\big)(1+x)^{|V(H)|}+D(H,x)\Big],\]where each clique \(C_i \in \mathcal{C}\) has \(n_i\) vertices. As anapplication, we study the \(\mathcal{D}\)-equivalence classes of somefamilies of graphs and, in particular, describe completely the\(\mathcal{D}\)-equivalence classes of friendship graphs constructed bycoalescing \(n\) copies of a cycle graph of length 3 with a common vertex. Lugansk National Taras Shevchenko University 2020-02-10 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/401 Algebra and Discrete Mathematics; Vol 28, No 2 (2019) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/401/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/401/643 Copyright (c) 2020 Algebra and Discrete Mathematics |
| spellingShingle | domination polynomial \(\mathcal{D}\)-equivalence class clique cover friendship graphs 05C60 05C69 Jahari, Somayeh Alikhani, Saeid Domination polynomial of clique cover product of graphs |
| title | Domination polynomial of clique cover product of graphs |
| title_full | Domination polynomial of clique cover product of graphs |
| title_fullStr | Domination polynomial of clique cover product of graphs |
| title_full_unstemmed | Domination polynomial of clique cover product of graphs |
| title_short | Domination polynomial of clique cover product of graphs |
| title_sort | domination polynomial of clique cover product of graphs |
| topic | domination polynomial \(\mathcal{D}\)-equivalence class clique cover friendship graphs 05C60 05C69 |
| topic_facet | domination polynomial \(\mathcal{D}\)-equivalence class clique cover friendship graphs 05C60 05C69 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/401 |
| work_keys_str_mv | AT jaharisomayeh dominationpolynomialofcliquecoverproductofgraphs AT alikhanisaeid dominationpolynomialofcliquecoverproductofgraphs |