The graph reconstruction number
β Scribed by Frank Harary; Michael Plantholt
- Publisher
- John Wiley and Sons
- Year
- 1985
- Tongue
- English
- Weight
- 177 KB
- Volume
- 9
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Dedicated ro the memory of Stan Ulam (31.
π SIMILAR VOLUMES
## Abstract The paper contains a proof of the conjecture of Harary and Plantholt, stated in the title.
## Abstract Suppose that __G, H__ are infinite graphs and there is a bijection Ξ¨; V(G) Ξ¨ V(H) such that __G__ β ΞΎ β H β Ξ¨(ΞΎ) for every ΞΎ βΌ __V__(G). Let __J__ be a finite graph and /(Ο) be a cardinal number for each Ο β __V__(J). Suppose also that either /(Ο) is infinite for every Ο β __V__(J) or _
We prove that the degree sequence of an infinite graph is reconstructibjle from its family of vertex-deleted subgraphs. Furthermore, as another result concerning the reconstruction of infinite graphs, we prove that the number c(G) of components of an infinite graph G is re~ons~uct~b~e if there is at
A set of points S of a graph is convex if any geodesic joining two points of S lies entirely within S. The convex hull of a set T of points is the smallest convex set that contains T. The hull number (h) of a graph is the cardinality of the smallest set of points whose convex hull is the entire grap