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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Мова: | English |
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Lugansk National Taras Shevchenko University
2020
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Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua: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 |
institution |
Algebra and Discrete Mathematics |
baseUrl_str |
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datestamp_date |
2020-02-10T19:12:26Z |
collection |
OJS |
language |
English |
topic |
domination polynomial \(\mathcal{D}\)-equivalence class clique cover friendship graphs 05C60 05C69 |
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 |
topic_facet |
domination polynomial \(\mathcal{D}\)-equivalence class clique cover friendship graphs 05C60 05C69 |
format |
Article |
author |
Jahari, Somayeh Alikhani, Saeid |
author_facet |
Jahari, Somayeh Alikhani, Saeid |
author_sort |
Jahari, Somayeh |
title |
Domination polynomial of clique cover product of graphs |
title_short |
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_sort |
domination polynomial of clique cover product of graphs |
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. |
publisher |
Lugansk National Taras Shevchenko University |
publishDate |
2020 |
url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/401 |
work_keys_str_mv |
AT jaharisomayeh dominationpolynomialofcliquecoverproductofgraphs AT alikhanisaeid dominationpolynomialofcliquecoverproductofgraphs |
first_indexed |
2025-07-17T10:32:40Z |
last_indexed |
2025-07-17T10:32:40Z |
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