ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2019: 0.755

SCImago Journal Rank (SJR) 2019: 0.600

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

Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 25(1-2) (2005) 167-182
DOI: 10.7151/dmgt.1270


Stanisław Bylka

Institute of Computer Science
Polish Academy of Sciences
21 Ordona street, 01-237 Warsaw, Poland


Families of all sets of independent vertices in graphs are investigated. The problem how to characterize those infinite graphs which have arithmetically maximal independent sets is posed. A positive answer is given to the following classes of infinite graphs: bipartite graphs, line graphs and graphs having locally infinite clique-cover of vertices. Some counter examples are presented.

Keywords: infinite graph, independent set, arithmetical maximal set, line graph.

2000 Mathematics Subject Classification: 05C69, 05C65, 05D05.


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Received 28 November 2003
Revised 8 March 2005