Rigidity and reconstruction for graphs
classification
🧮 math.CO
math.MG
keywords
graphgraphsrigiditytermsb-regularbettiboundaryclosed
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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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