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On Moore Graphs with Diameters 2 and 3
Abstract
This note treats the existence of connected, undirected graphs homogeneous of degree d and of diameter k, having a number of nodes which is maximal according to a certain definition. For k = 2 unique graphs exist for d = 2,3,7 and possibly for d = 57 (which is undecided), but for no other degree. For k = 3 a graph exists only for d = 2. The proof exploits the characteristic roots and vectors of the adjacency matrix (and its principal submatrices) of the graph.
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Cited by
A recursive approach to low complexity codes
Tanner, R. (1981) · IEEE Transactions on Information Theory · doi:10.1109/tit.1981.1056404 · Cited by 3,138
Biggs, N. (1974) · doi:10.1017/cbo9780511608704 · Cited by 2,940
Metadata
- Authors
- Hoffman, A. J., & Singleton, R. R.
- Venue
- IBM Journal of Research and Development
- Publisher
- IBM
- Published
- 1960-11
- Volume
- 4
- Issue
- 5
- Pages
- 497-504
- ISSN
- 0018-8646 (ISSN-L)
- OpenAlex
- W1981159511
- Cited by
- 489
- References
- 0
- FWCI
- 1.51
- Type
- journal article
- Language
- en
- Open access
- closed
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- Hoffman, A. J., & Singleton, R. R. (1960). On Moore Graphs with Diameters 2 and 3. IBM Journal of Research and Development. https://doi.org/10.1147/rd.45.0497
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
