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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2024.9
- 수록면
- 499 - 504 (6page)
- DOI
- 10.5666/KMJ.2024.64.3.499
이용수
초록· 키워드
오류제보하기
Let Γ be a distance-regular graph with valency k and diameter D ≥ 3. It has been shown that for a fixed real number α > 2, if Γ has at most αk vertices, then there are only finitely many such graphs, except for the cases where (D = 3 and Γ is imprimitive) and (D = 4 and Γ is antipodal and bipartite). And there is a classification for α ≤ 3. In this paper, we further study such distance-regular graphs for α > 3. Let β ≥ 3 be an integer, and let Γ be a distance-regular graph with valency k, diameter D ≥ 3 and at most βk + 1 vertices. Note that if D ≥ β + 1, then Γ must have at least βk + 2 vertices. Thus, the assumption that Γ has at most βk + 1 vertices implies that D ≤ β. We focus on the case where D = β and provide a classification of distance-regular graphs having at most Dk + 1 vertices.
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