Edge ideals of squares of trees

We describe all the trees with the property that the corresponding edge ideal of the square of the tree has a linear resolution. As a consequence, we give a complete characterization of those trees $T$ for which the square is co-chordal, that is the complement of the square, $(T^2)^c$, is a chordal graph. For particular classes of trees such as paths and double brooms we determine the Krull dimension and the projective dimension.

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