Leaps: an approach to the block structure of a graph
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).
Mulder, H.M., & Nebesky, L.. (2004). Leaps: an approach to the block structure of a graph (No. EI 2004-49). Report / Econometric Institute, Erasmus University Rotterdam. Retrieved from http://hdl.handle.net/1765/1827