논문KCI 등재
A Relationship between the Second Largest Eigenvalue and Local Valency of an Edge-regular Graph
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For a distance-regular graph with valency k, second largest eigenvalue r and diameter D. compare this number with the local valency to give a relationship between the second largest eigenvalue and the local valency. Also, we apply these relationships to distance-regular graphs.
Abstract
For a distance-regular graph with valency k, second largest eigenvalue r and diameter D. compare this number with the local valency to give a relationship between the second largest eigenvalue and the local valency. Also, we apply these relationships to distance-regular graphs.
참고문헌 (7)
- A. E. Brouwer, "Distance-Regular Graphs" (1989), SpringerVerlag
- A. E. Brouwer, "Spectra of Graphs, Universitext" (2012), Springer
- E. R. van Dam, "Spectral characterizations of some distanceregular graphs", Journal of Algebraic Combinatorics, 15, pp.189~202 (2002)
- J. H. Koolen, "Shilla distance-regular graphs", European Journal of Combinatorics, 31, pp.2064~2073 (2010)
- J. H. Koolen, "Distance-regular graphs with a1 or c2 at least half the valency", Journal of Combinatorial Theory, Series A, 119, pp.546~555 (2012)
- J. H. Koolen, "An inequality involving the second largest and smallest eigenvalue of a distance-regular graph", Linear Algebra and its Applications, 434, pp.2404~2412 (2011)
- J. Park, "The distance-regular graphs with valency k ≥ 2, diameter D ≥ 3 and kD−1 +kD ≤ 2k", Discrete Mathematics, 340, pp.550~561 (2017)
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