Partitioning a graph into a dominating set, a total dominating set, and something else | Zendy

Michael A. Henning | Zendy; Christian Löwenstein | Zendy; Dieter Rautenbach | Zendy

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Partitioning a graph into a dominating set, a total dominating set, and something else

Author(s) -

Michael A. Henning,

Christian Löwenstein,

Dieter Rautenbach

Publication year - 2010

Publication title -

discussiones mathematicae graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.476

H-Index - 19

eISSN - 2083-5892

pISSN - 1234-3099

DOI - 10.7151/dmgt.1514

Subject(s) - dominating set , mathematics , combinatorics , graph , connected dominating set , set (abstract data type) , discrete mathematics , computer science , vertex (graph theory) , programming language

A recent result of Henning and Southey (A note on graphs with disjoint dominating and total dominating set, {\it Ars Comb.} {\bf 89} (2008), 159--162) implies that every connected graph of minimum degree at least three has a dominating set $D$ and a total dominating set $T$ which are disjoint. We show that the Petersen graph is the only such graph for which $D\cup T$ necessarily contains all vertices of the graph.

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