Leaps: an approach to the block structure of a graph

Martyn Mulder and L. Nebesky

No EI 2004-49, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute

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 LG of the connected graph G. The underlying graph of +G , as well as that of LG , 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).

Date: 2004-12-20
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