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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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Chellai et al.~\cite{1} gave an upper bound on the $[1, 2]$-domination number of tree and posed an open question ``how to classify trees satisfying the sharp bound?". Yang and Wu ~\cite{5} gave a partial solution for tree of order $n$ with $\ell$-leaves such that every non-leaf vertex has degree at least 4. In this paper, we give a new upper bound on the $[1, 2]$-domination number of tree which extends the result of Yang and Wu. In addition, we design a polynomial time algorithm for solving the open question. By using this algorithm, we give a characterization on the $[1, 2]$-domination number for trees of order $n$ with $\ell$ leaves satisfying $n-\ell$. Thereby, the open question posed by Chellai et al. is solved.
목차
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참고문헌 (5)
참고문헌 신청
A. T. Amin / 1992 / Neighborhood domination with parity restrictions in graphs / Congr. Numer. 91:19~30
A. T. Amin / 1996 / All parity realizable trees / J. Combin. Math. Combin. Comput. 20:53~63
M. Chellali / 2013 / [1, 2]-sets in graphs / Discrete Appl. Math. 161(18):2885~2893
I. J. Dejter / 2009 / Quasiperfect domination in triangular lattices / Discuss. Math. Graph Theory 29(1):179~198
X. Yang / 2014 / [1, 2]-domination in graphs / Discrete Appl. Math. 175:79~86
A. T. Amin / 1996 / All parity realizable trees / J. Combin. Math. Combin. Comput. 20:53~63
M. Chellali / 2013 / [1, 2]-sets in graphs / Discrete Appl. Math. 161(18):2885~2893
I. J. Dejter / 2009 / Quasiperfect domination in triangular lattices / Discuss. Math. Graph Theory 29(1):179~198
X. Yang / 2014 / [1, 2]-domination in graphs / Discrete Appl. Math. 175:79~86
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