DMGT

Discussiones Mathematicae Graph Theory 26(1) (2006) 77-90
DOI: https://doi.org/10.7151/dmgt.1303

LEAPS: AN APPROACH TO THE BLOCK STRUCTURE OF A GRAPH

Henry Martyn Mulder

Econometrisch Instituut, Erasmus Universiteit
P.O. Box 1738, 3000 DR Rotterdam, The Netherlands
e-mail: hmmulder@few.eur.nl

Ladislav Nebeský

Filozofická Fakulta, Univerzita Karlova v Praze
J. Palacha 2, 116 38 Praha 1, Czech Republic
e-mail: Ladislav.Nebesky@ff.cuni.cz

Abstract

To study the block structure of a connected graph G = (V,E), we introduce two algebraic approaches that reflect this structure: a binary operation + called a leap operation and a ternary relation L called a leap system, both on a finite, nonempty set V. These algebraic structures are easily studied by considering their underlying graphs, which turn out to be block graphs. Conversely, we define the operation +_G as well as the set of leaps L_G of the connected graph G. The underlying graph of +_G, as well as that of L_G, turns out to be just the block closure of G (i.e., the graph obtained by making each block of G into a complete subgraph).

Keywords: leap, leap operation, block, cut-vertex, block closure, block graph.

2000 Mathematics Subject Classification: 05C99, 05C75, 08A99.

References

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Received 14 January 2005
Revised 20 June 2005