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Unicyclic Graphs Satisfy Harary′s Conjecture

Published online by Cambridge University Press:  20 November 2018

E. Arjomandi  and
D. G. Corneil
E. Arjomandi
Affiliation:
Department of Computer Science, University of Toronto, Toronto, Canada
D. G. Corneil
Affiliation:
Department of Computer Science, University of Toronto, Toronto, Canada
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Ulam in [7] has conjectured that any graph G with p≥3 nodes is uniquely reconstructable from its collection of subgraphs Gi=G-vi, i=1,2, … p. This conjecture has been proved for various finite graphs including regular, Eulerian, unicyclic, separable, trees and cacti. Since Ulam′s conjecture seems difficult to prove or disprove, some authors have tried to strengthen the conjecture [3]. One of these stronger conjectures is Harary′s conjecture [2].

Keywords

0540Ulam′s ConjectureHarary′s Conjectureunicyclic graphsreconstruction of graphs
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 4 , 01 December 1974 , pp. 593 - 595
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Arjomandi, E., Some Results on Ulam's Conjecture, M.Sc. thesis, University of Toronto, Department of Computer Science, (1972).Google Scholar
2. Harary, F., On the reconstruction of a graph from a collection of subgraphs. Theory of graphs and its Applications (M. Fielder, ?d.), Prague, (1964), 47-52. Reprinted Academic Press, New York (1964).Google Scholar
3. Manvel, B., On reconstruction of graphs. Conference in Graph Theory. The Many Facets of Graph Theory (C. T. Chartrand and S. F. Kapoor, eds.), Springer-Verlag, New York (1969), 207-214.Google Scholar
4. Manvel, B., Reconstruction of trees, Can. J. Math. 22, (1970), 55-60.Google Scholar
5. Manvel, B., On Reconstruction of Graphs, Ph.D. thesis, University of Michigan, (1970).Google Scholar
6. Manvel, B., Reconstruction of unicyclic graphs, Proof Techniques in Graph Theory (F. Harary, ?d.), Academic Press, New York (1969), 103-107.Google Scholar
7. Ulam, S.M., A collection of mathematical problems, Wiley (Interscience), New York (1960).Google Scholar