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arXiv · 1412.8203

A New Upper Bound on Total Domination Number of Bipartite Graphs

Saieed Akbari·Pooyan Ehsani·Sahar Qajar·Ali Shameli·Hadi Yami
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Abstract

Let $ G $ be a graph. A subset $S \subseteq V(G) $ is called a total dominating set if every vertex of $G$ is adjacent to at least one vertex of $S$. The total domination number, $γ_{t}$($G$), is the minimum cardinality of a total dominating set of $G$. In this paper using a greedy algorithm we provide an upper bound for $γ_{t}$($G$), whenever $G$ is a bipartite graph and $δ(G)$ $\geq$ $k$. More precisely, we show that if $k$ > 1 is a natural number, then for every bipartite graph $G$ of order $n$ and $δ(G) \ge k$, $ $$γ_{t}$($G$) $\leq$ $n(1- \frac{k!}{\prod_{i=0}^{k-1}(\frac{k}{k-1}+i)}).$

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Saieed Akbari, Pooyan Ehsani, Sahar Qajar, Ali Shameli, Hadi Yami. 2014-12-28. A New Upper Bound on Total Domination Number of Bipartite Graphs. https://arxiv.org/abs/1412.8203

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