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On a reconstruction problem

✍ Scribed by Bhalchandra D. Thatte

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 86 KB
Volume: 137
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)e0151-s

No coin nor oath required. For personal study only.

✦ Synopsis

This note supplements an earlier paper of this author, in which the concept of a strong k-hypomorphism between two graphs was defined (Thatte, 1990, Section VI). For k = 1, this is just a hypomorphism. Here it is proved that strongly k-hypomorphic graphs and strongly k-edge hypomorphic directed graphs are isomorphic if k > 1.

Graphs in this note are directed or undirected. By V(G), E(G) and [G] we will denote, respectively, the vertex set, the edge set and the isomorphism class of a graph G. Let

Ek(G)={E~_E(G):

[El=k} and Vk(G)={W~ V(G): IWl=k}.

The following problem was posed in Section VI of .

Let G and H be two m-edge and n-vertex graphs. Let there

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