On Trees as Star Complements in Regular Graphs
Let G be a connected r-regular graph (r ---gt--- 3) of order n with a tree of order t as a star complement for an eigenvalue µ ∉ {−1, 0}. It is shown that n ≤ 1/2 (r + 1)t − 2. Equality holds when G is the complement of the Clebsch graph (with µ = 1, r = 5, t = 6, n = 16).
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| Format: | Article |
| Language: | English |
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Sciendo
2020-05-01
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| Series: | Discussiones Mathematicae Graph Theory |
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| Online Access: | https://doi.org/10.7151/dmgt.2272 |