Minus domination number in cubic graph |
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Authors: | Liying Kang Maocheng Cai |
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Affiliation: | (1) Department of Basic Course, Shijiazhuang Railway Institute, 050043, China;(2) Present address: Institute of Systems Science, Chinese Aeademy of Sciences, 100080 Beijing, China;(3) Asian-Pacific Operations Research Center, China |
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Abstract: | An upper bound is established on the parameter Γ− (G) for a cubic graphG and two infinite families of 3-connected graphs Gk, Gk* are constructed to show that the bound is sharp and, moreover, the difference Γ−(Gk*)-γs(Gk*) can be arbitrarily large, where Γ−(Gk*) and γs(Gk*) are the upper minus domination and signed domination numbers of Gk*, respectively. Thus two open problems are solved. |
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Keywords: | cubic graph minus domination signed domination |
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