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In this paper, some subclasses of block graphs are considered in order toanalyze Fiedler vector of its members. Two families of block graphs withcliques of fixed size, the block-path and block-starlike graphs, areintroduced. Cases A and B of classification for both families were considered,as well as the behavior of the algebraic connectivity for particular cases ofblock-path graphs.

Fiedler vector analysis for particular cases of connected graphs