Stronger reconstruction of distance-hereditary graphs
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CitationPriya, P. D. & Monikandan, S. (2021). Stronger reconstruction of distance-hereditary graphs. TWMS Journal of Applied and Engineering Mathematics, 11(SI), 25-29.
A graph is said to be set-reconstructible if it is uniquely determined up to isomorphism from the set S of its non-isomorphic one-vertex deleted unlabeled subgraphs. Harary’s conjecture asserts that every finite simple undirected graph on four or more vertices is set-reconstructible. A graph G is said to be distance-hereditary if for all connected induced subgraph F of G, dF (u, v) = dG(u, v) for every pair of vertices u, v ∈ V (F). In this paper, we have proved that the class of all 2-connected distance-hereditary graphs G with diam(G) = 2 or diam(G) = diam(Ḡ) = 3 are set-reconstructible.
SourceTWMS Journal of Applied and Engineering Mathematics
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