ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2018-2019): c. 84%

Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 30(3) (2010) 377-383
DOI: 10.7151/dmgt.1500


Joanna Cyman

Department of Technical Physics and Applied Mathematics
Gdańsk University of Technology
Narutowicza 11/12, 80-952 Gdańsk, Poland


Let G = (V,E) be a graph. Set D ⊆ V(G) is a total outer-connected dominating set of G if D is a total dominating set in G and G[V(G)−D] is connected. The total outer-connected domination number of G, denoted by γtc(G), is the smallest cardinality of a total outer-connected dominating set of G. We show that if T is a tree of order n, then γtc(T) ≥ ⎡[2n/3]⎤. Moreover, we constructively characterize the family of extremal trees T of order n achieving this lower bound.

Keywords: total outer-connected domination number, domination number.

2010 Mathematics Subject Classification: 05C05, 05C69.


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Received 18 March 2009
Revised 27 July 2009
Accepted 17 August 2009