# Graph structure having maximum algebraic connectivity among some given blocks

using this code we get a graph on 4 blocks of which 3 are pendant block(pendant in the sense that it has exactly one cut vertex).Now can we have some sage code that gives all connected graphs with these 4block of which exactly 3 blocks are pendant and also among those collection we need that graph having maximum algebraic conectivity

G=graphs.EmptyGraph()

G.add_edges([(1,2),(2,3),(1,3),(3,4),(4,5),(5,6),(6,7),(7,8),(8,5),(5,7),(8,6),(5,9),(9,10),(10,11),(11,12),

(12,9),(9,13),(13,14),(14,3)])

G.show()