Inequalities involving independence domination, f-domination, connected and total f-domination numbers |
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Authors: | Sanming Zhou |
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Institution: | (1) Department of Mathematics and Statistics, The University of Western Australia, Nedlands, Perth, WA 6907, Australia |
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Abstract: | Let f be an integer-valued function defined on the vertex set V(G) of a graph G. A subset D of V(G) is an f-dominating set if each vertex x outside D is adjacent to at least f(x) vertices in D. The minimum number of vertices in an f-dominating set is defined to be the f-domination number, denoted by
f
(G). In a similar way one can define the connected and total f-domination numbers
c,f
(G) and
t,f
(G). If f(x) = 1 for all vertices x, then these are the ordinary domination number, connected domination number and total domination number of G, respectively. In this paper we prove some inequalities involving
f
(G),
c,f
(G),
t,f
(G) and the independence domination number i(G). In particular, several known results are generalized. |
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Keywords: | domination number independence domination number f-domination number connected f-domination number total f-domination number |
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