Edge growth in graph powers
Pokrovskiy, Alexey (2013) Edge growth in graph powers. Australasian Journal of Combinatorics 58 (2), pp. 347-357. ISSN 2202-3518.
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Official URL: https://ajc.maths.uq.edu.au/pdf/58/ajc_v58_p347.pd...
Abstract
For a graph G, its rth power G^r has the same vertex set as G, and has an edge between any two vertices within distance r of each other in G. We give a lower bound for the number of edges in the rth power of G in terms of the order of G and the minimal degree of G. As a corollary we determine how small the ratio e(G^r)/e(G) can be for regular graphs of diameter at least r.
Metadata
| Item Type: | Article |
|---|---|
| School: | Birkbeck Faculties and Schools > Faculty of Business and Law > Birkbeck Business School |
| Depositing User: | Alexey Pokrovskiy |
| Date Deposited: | 21 Jan 2019 15:51 |
| Last Modified: | 02 Aug 2023 17:47 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/25903 |
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