On open problems on the connected bicritical graphs

On open problems on the connected bicritical graphs

In the paper [1], the following problems have been proposed. Is it true that every connected bicritical graph has a minimum dominating set containing any two specified vertices of the graphs? Is it true if G is a connected bicritical graph, then [gamma](G) = i(G) , where i(G) is the independent domi...

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Veröffentlicht in:Scientia magna 2013-03, Vol.9 (1), p.72-72
Hauptverfasser: Mojdeh, D.A, Ahangar, H. Abdollahzadeh, Karimizad, S.S
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Graphic methods
Graphs
Symbols
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Zusammenfassung:In the paper [1], the following problems have been proposed. Is it true that every connected bicritical graph has a minimum dominating set containing any two specified vertices of the graphs? Is it true if G is a connected bicritical graph, then [gamma](G) = i(G) , where i(G) is the independent domination number? We disprove the second problem and show the truth of the first problem for a certain family of graphs. Furthermore this family of graphs is characterized with respect to bicriticality, diameter, vertex connectivity and edge connectivity.
ISSN:1556-6706