Rigidity and reconstruction for graphs

Published 29 Jan 2016 in math.CO and math.MG | (1601.08130v1)

Abstract: We present measure theoretic rigidity for graphs of first Betti number b>1 in terms of measures on the boundary of a 2b-regular tree, that we make explicit in terms of the edge-adjacency and closed-walk structure of the graph. We prove that edge-reconstruction of the entire graph is equivalent to that of the "closed walk lengths".

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