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In this paper, we consider several domination parameters like perfect domination number, locating-domination number, open-locating-domination number, etc.~in the Mycielski graph $M(G)$ of a graph $G$. We found upper bounds for locating-domination number of $M(G)$ and computational formulae for perfect locating-domination number and open locating-domination number of $M(G)$. We also showed that the perfect domination number of $M(G)$ is at least that of $G$ plus $1$ and that for each positive integer $n$, there exists a graph $G_n$ such that the perfect domination number of $M(G_n)$ is equal to that of $G_n$ plus $n$.
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참고문헌 (8)
참고문헌 신청
Gerard J. Chang / 1999 / Circular chromatic numbers of Mycielski's graphs / Discrete Mathematics 205(1-3):23~37
Genghua Fan / 2004 / Circular Chromatic Number and Mycielski Graphs / Combinatorica 24(1):127~135
Michael Larsen / 1995 / The fractional chromatic number of mycielski's graphs / Journal of Graph Theory 19(3):411~416
Wensong Lin / 2006 / Several parameters of generalized Mycielskians / Discrete Applied Mathematics 154(8):1173~1182
Daphne Der-Fen Liu / 2004 / Circular chromatic number for iterated Mycielski graphs / Discrete Mathematics 285(1-3):335~340
Genghua Fan / 2004 / Circular Chromatic Number and Mycielski Graphs / Combinatorica 24(1):127~135
Michael Larsen / 1995 / The fractional chromatic number of mycielski's graphs / Journal of Graph Theory 19(3):411~416
Wensong Lin / 2006 / Several parameters of generalized Mycielskians / Discrete Applied Mathematics 154(8):1173~1182
Daphne Der-Fen Liu / 2004 / Circular chromatic number for iterated Mycielski graphs / Discrete Mathematics 285(1-3):335~340
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