Leaps: an approach to the block structure of a graph
2004-12-20
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
