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Graph having largest algebraic connectivity among some given blocks

Suppose we are given some blocks(in sense of graph theory). Now suppose we have to find out that graph(connected) which has maximum algebraic connectivity and consists of those given blocks. the blocks may be path graph,cycle etc.please explain with a sage code.

Graph having largest algebraic connectivity among some given blocks

Suppose we are given some blocks(in sense of graph theory). Now suppose we have to find out that graph(connected) which has maximum algebraic connectivity and consists of those given blocks. the blocks may be path graph,cycle etc.please explain with a sage code.