Geodesic
Unicyclic Graphs Satisfy Harary′s Conjecture
Canadian mathematical bulletin, Tome 17 (1974) no. 4, pp. 593-595

Voir la notice de l'article provenant de la source Cambridge University Press

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].
DOI : 10.4153/CMB-1974-106-9
Mots-clés : 0540, Ulam′s Conjecture, Harary′s Conjecture, unicyclic graphs, reconstruction of graphs 
Arjomandi, E.; Corneil, D. G. Unicyclic Graphs Satisfy Harary′s Conjecture. Canadian mathematical bulletin, Tome 17 (1974) no. 4, pp. 593-595. doi: 10.4153/CMB-1974-106-9
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[1] 1. Arjomandi, E., Some Results on Ulam's Conjecture, M.Sc. thesis, University of Toronto, Department of Computer Science, (1972). Google Scholar

[2] 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

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[5] 5. Manvel, B., On Reconstruction of Graphs, Ph.D. thesis, University of Michigan, (1970). Google Scholar

[6] 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] 7. Ulam, S.M., A collection of mathematical problems, Wiley (Interscience), New York (1960). Google Scholar

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