Forests and trees among Gallai graphs

Forests and trees among Gallai graphs

The Gallai graph Gal(G) of a graph G has the edges of G as its vertices, and two distinct vertices e and f of Gal(G) are adjacent in Gal(G) if the edges e and f of G are adjacent in G but do not span a triangle in G. In the present paper we characterize those graphs whose Gallai graphs are forests o...

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Veröffentlicht in:Discrete mathematics 2015-02, Vol.338 (2), p.190-195
Hauptverfasser: Joos, Felix, Le, Van Bang, Rautenbach, Dieter
Format: Artikel
Sprache:eng
Schlagworte:
Anti-Gallai graph
Forests
Gallai graph
Graph theory
Graphs
Line graph
Mathematical analysis
Trees
Triangles
Triangular line graph
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Zusammenfassung:The Gallai graph Gal(G) of a graph G has the edges of G as its vertices, and two distinct vertices e and f of Gal(G) are adjacent in Gal(G) if the edges e and f of G are adjacent in G but do not span a triangle in G. In the present paper we characterize those graphs whose Gallai graphs are forests or trees, respectively.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2014.09.003