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Reconstructibility of $$k$$-distance-local subgraphs rooted at a subgraph. (Chinese. English summary) Zbl 1012.05117
Summary: A $$k$$-distance-local subgraph rooted at a subgraph of a graph is defined and it is proved that the number of $$k$$-distance-local subgraphs of a graph $$G$$ which are isomorphic to a given $$k$$-distance-local subgraph rooted at a subgraph is reconstructible. Therefore the results in [L. Xie and H. Fan, Adv. Math., Beijing 26, 440-444 (1997; Zbl 0908.05066)] are generalized.
##### MSC:
 05C60 Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)