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Reconstruction of Cacti

Published online by Cambridge University Press:  20 November 2018

Dennis Geller  and
Bennet Manvel
Dennis Geller
Affiliation:
The University of Michigan, Ann Arbor, Michigan
Bennet Manvel
Affiliation:
The University of Michigan, Ann Arbor, Michigan
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Following the work of Kelly (8), Harary and Palmer (5), and Bondy (1) on the reconstruction of trees, and of Manvel (10) on the reconstruction of connected graphs with a single cycle, it was a natural step to attempt to solve the reconstruction problem for cacti. The solution of this problem, presented here, assumes both Kelly's Theorem and the result of Manvel in (10). Any definitions not given here can be found in (2).

Let graph G have point set V = {v1 v2, …, vp} and line set X = {x1, x2, …, xq}. For each vi ∈ V, Gi = G – vi is the maximal subgraph of G which does not contain vi and is formed by deleting vi and all lines incident with it from G.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 1354 - 1360
Copyright
Copyright © Canadian Mathematical Society 1969

References

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