http://hdl.handle.net/1765/1827
series: EI 2004-49

# Leaps: an approach to the block structure of a graph

### Mulder, H.M. Nebesky, L.

Research Paper
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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).

Automatically Extracted Terms
• graph
• block
• operation
• leap operation
• access operation
• block graph
• vertice
• vertex
• cut-vertex
• definition
• leap system
• graph g
• theorem
• proof
• access
• system
• function
• axiom
• ternary relation
• nonempty