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We obtain an improved lower bound for the regularity of the binomial edgeideals of trees. We prove an upper bound for the regularity of the binomialedge ideals of certain subclass of block-graphs. As a consequence we obtainsharp upper and lower bounds for the regularity of binomial edge ideals of aclass of trees called lobsters. We also obtain precise expressions for theregularities of binomial edge ideals of certain classes of trees and blockgraphs.

Regularity of Binomial Edge Ideals of Certain Block Graphs