Graph Exponentiation and Neighborhood Reconstruction
Any graph G admits a neighborhood multiset 𝒩(G) = {NG(x) | x ∈ V (G)} whose elements are precisely the open neighborhoods of G. We say G is neighborhood reconstructible if it can be reconstructed from 𝒩(G), that is, if G ≅ H whenever 𝒩 (G) = 𝒩(H) for some other graph H. This note characterizes neigh...
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2021-02-01
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| Series: | Discussiones Mathematicae Graph Theory |
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| Online Access: | https://doi.org/10.7151/dmgt.2186 |
| Summary: | Any graph G admits a neighborhood multiset 𝒩(G) = {NG(x) | x ∈ V (G)} whose elements are precisely the open neighborhoods of G. We say G is neighborhood reconstructible if it can be reconstructed from 𝒩(G), that is, if G ≅ H whenever 𝒩 (G) = 𝒩(H) for some other graph H. This note characterizes neighborhood reconstructible graphs as those graphs G that obey the exponential cancellation GK2 ≅ HK2 ⇒ G ≅= H. |
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| ISSN: | 2083-5892 |