Geodesic
Enumeration of labeled bi-block graphs
Diskretnyj analiz i issledovanie operacij, Tome 30 (2023) no. 4, pp. 24-34.

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A bi-block graph is a connected graph in which all blocks are complete bipartite graphs. Labeled bi-block graphs and bridgeless bi-block graphs are enumerated exactly and asymptotically by the number of vertices. It is proved that almost all labeled connected bi-block graphs have no bridges. In addition, planar bi-block graphs are enumerated, and an asymptotic estimate is found for the number of such graphs. Tab. 1, bibliogr. 12.
Keywords: enumeration, labeled graph, bridgeless graph, complete bipartite graph, planar graph, block, bi-block graph, random graph, asymptotics. 
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V. A. Voblyi. Enumeration of labeled bi-block graphs. Diskretnyj analiz i issledovanie operacij, Tome 30 (2023) no. 4, pp. 24-34. http://geodesic.mathdoc.fr/item/DA_2023_30_4_a1/

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