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
Автори: Jahari, Somayeh, Alikhani, Saeid
Формат: Стаття
Мова:English
Опубліковано: Lugansk National Taras Shevchenko University 2020
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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
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spelling 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
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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