Geodesic
Leaps: an approach to the block structure of a graph
Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 1, pp. 77-90

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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 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 
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Mulder, Henry; Nebeský, Ladislav. Leaps: an approach to the block structure of a graph. Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 1, pp. 77-90. http://geodesic.mathdoc.fr/item/DMGT_2006_26_1_a7/