A Revisit on Independent Outer-connected Domination in Graphs

Jocecar Lomarda-Hinampas

Abstract


A dominating set S is an independent outer-connected dominating set of G if S is an independent dominating set of G and the subgraph hV (G) \ Si is connected. The independent outer-connected domination number of G denoted by γeic(G), is the cardinality of the smallest independent outer-connected dominating set of G. An independent outer-connected dominating set of G with cardinality equal to γeic(G) is called γeic-set of G. This paper presents some realization problems on independent outer-connected domination in graphs and shows that the difference of the parameters can be made arbitrarily large.

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