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A New Upper Bound on Total Domination Number of Bipartite Graphs
- Publication Year :
- 2014
-
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, $\gamma_{t}$($G$), is the minimum cardinality of a total dominating set of $G$. In this paper using a greedy algorithm we provide an upper bound for $\gamma_{t}$($G$), whenever $G$ is a bipartite graph and $\delta(G)$ $\geq$ $k$. More precisely, we show that if $k$ > 1 is a natural number, then for every bipartite graph $G$ of order $n$ and $\delta(G) \ge k$, $ $$\gamma_{t}$($G$) $\leq$ $n(1- \frac{k!}{\prod_{i=0}^{k-1}(\frac{k}{k-1}+i)}).$<br />Comment: 10 pages, journal
- Subjects :
- Mathematics - Combinatorics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1412.8203
- Document Type :
- Working Paper