We study the least doubling constant CG among all possible doubling measures defined on a path graph G. We consider both finite and infinite cases and show that if G=Z, CZ=3, while for G=Ln the path graph with n vertices, one has 1+2cos(π n+1)≤CLn<3, with equality on the lower bound if and only if n≤8. Moreover, we analyze the structure of doubling minimizers on Ln and Z—those measures whose doubling constant is the smallest possible.
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Durand-Cartagena et al. (2024) studied this question.
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