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## On the bondage, strong and weak bondage numbers in Complementary Prism Graphs

Authors: Aysun Aytaç, Tufan Turaci
Keywords: Connectivity, Domination number, Strong and weak domination numbers, Bondage number, Strong and weak bondage numbers, Complementary prism graphs.

### Abstract

Let $G =(V(G),E(G))$ be a simple undirected graph of order $n$, and let $S \subseteq V(G)$. If every vertex in $V(G)-S$ is adjacent to at least one vertex in $S$, then the set $S$ is called a \textit{dominating set}. The \textit{domination number} of $G$ is the minimum cardinality taken over all sets of $S$, and it is denoted by $\gamma(G)$. Recently, the effect of one or more edges deletion on the domination number has been examined in many papers. Let $F\subseteq E(G)$. The \textit{bondage number} $b(G)$ of $G$ is the minimum cardinality taken over all sets of $F$ such that $\gamma(G-F) > \gamma(G)$. In the literature, a lot of domination and bondage parameters have been defined depending on different properties. In this paper, we investigate the \emph{bondage, strong and weak bondage numbers} of complementary prism graphs of some well-known graph families.

Aysun Aytaç
Ege University, Science Faculty, Mathematics Dept.
Bornova-IZMIR-TURKEY
Phone:+90 232 311 17 45
E-mail:

Tufan Turacı
Department of Computer Engineering, Faculty of Engineering,
Pamukkale University
20160, Denizli/TURKEY
E-mail:
Phone: +90 258 296 30 62

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