Domination polynomial of clique cover product of graphs

• Date: 2020
• Main Authors: Jahari, Somayeh, Alikhani, Saeid
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2020
• Subjects: domination polynomial; \(\mathcal{D}\)-equivalence class; clique cover; friendship graphs; 05C60; 05C69
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/401
• Journal Title: Algebra and Discrete Mathematics

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 \(n_i\)...