Tight Upper Bounds for the Domination Numbers of Graphs with Given Order and Minimum Degree

Let $\gamma(n,\delta)$ denote the maximum possible domination number of a graph with $n$ vertices and minimum degree $\delta$. Using known results we determine $\gamma(n,\delta)$ for $\delta = 0, 1, 2, 3$, $n \ge \delta + 1$ and for all $n$, $\delta$ where $\delta = n-k$ and $n$ is sufficiently larg...

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Published in:The Electronic journal of combinatorics 1997-10, Vol.4 (1)
Main Authors: Clark, W. Edwin, Dunning, Larry A.
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Language:English
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description Let $\gamma(n,\delta)$ denote the maximum possible domination number of a graph with $n$ vertices and minimum degree $\delta$. Using known results we determine $\gamma(n,\delta)$ for $\delta = 0, 1, 2, 3$, $n \ge \delta + 1$ and for all $n$, $\delta$ where $\delta = n-k$ and $n$ is sufficiently large relative to $k$. We also obtain $\gamma(n,\delta)$ for all remaining values of $(n,\delta)$ when $n \le 14$ and all but 6 values of $(n,\delta)$ when $n = 15$ or 16.
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title Tight Upper Bounds for the Domination Numbers of Graphs with Given Order and Minimum Degree
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