The Domination Parameters of Cubic Graphs |
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| Authors: | Igor E Zverovich Vadim E Zverovich |
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| Institution: | (1) RUTCOR—Rutgers Center for Operations Research, Rutgers, The State University of New Jersey, Piscataway, NJ 08854-8003, USA;(2) Department of Mathematical Sciences, Brunel University, Uxbridge, Middlesex, UB8 3PH, UK |
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| Abstract: | Let ir(G),  (G), i(G),  0(G),  (G) and IR(G) be the irredundance number, the domination number, the independent domination number, the independence number, the upper domination number and the upper irredundance number of a graph G, respectively. In this paper we show that for any nonnegative integers k1, k2, k3, k4, k5 there exists a cubic graph G satisfying the following conditions: (G) – ir(G)  k1, i(G) – (G) k2, 0(G) – i(G) > k3, (G) – 0(G) – k4, and IR(G) – (G) – k5. This result settles a problem posed in 9].Supported by the INTAS and the Belarus Government (Project INTAS-BELARUS 97-0093).Supported by RUTCOR. |
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