Higher order connectivity index of starlike trees

We show that for every integer h ≥ 0, the higher order connectivity index hχ(T) of a starlike tree T (a tree with unique vertex of degree > 2) is completely determined by its branches of length ≤ h. As a consequence, we show that starlike trees which have equal h-connectivity index for all h ≥ 0 are isomorphic.

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