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A New Upper Bound on the Total Domination Number of a Graph

2007
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Electronic Journal of Combinatorics
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A set $S$ of vertices in a graph $G$ is a total dominating set of $G$ if every vertex of $G$ is adjacent to some vertex in $S$. The minimum cardinality of a total dominating set of $G$ is the total domination number of $G$. Let $G$ be a connected graph of order $n$ with minimum degree at least two and with maximum degree at least three. We define a vertex as large if it has degree more than $2$ and we let ${\cal L}$ be the set of all large vertices of $G$. Let $P$ be any component of $G - {\cal

doi:10.37236/983
fatcat:q2essurng5btjfnwx7otaqlf2u