Uniqueness of Graph Square Roots of Girth Six

Anna Adamaszek, Michał Adamaszek


We prove that if two graphs of girth at least $6$ have isomorphic squares, then the graphs themselves are isomorphic. This is the best possible extension of the results of Ross and Harary on trees and the results of Farzad et al. on graphs of girth at least $7$. We also make a remark on reconstruction of graphs from their higher powers.

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