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Two graphs   G   and   H   are  hypomorphic  if there exists a bijection    φ  :  V  (  G  )  →  V  (  H  )    such that    G  −  v  ≅  H  −  φ  (  v  )    for each    v  ∈  V  (  G  )   . A graph   G   is  reconstructible  if    H  ≅  G    for all   H   hypomorphic to   G  .  It is well known that not all infinite graphs are reconstructible. However, the Harary–Schwenk–Scott Conjecture from 1972 suggests that all locally finite trees are reconstructible.  In this paper, we construct a counterexample to the Harary–Schwenk–Scott Conjecture. Our example also answers four other questions of Nash‐Williams, Halin and Andreae on the reconstruction of infinite graphs.

A counterexample to the reconstruction conjecture for locally finite trees