There are Finitely Many Triangle-Free Distance-Regular Graphs with Degree 8, 9 or 10
J.H. Koolen
and V. Moulton2
2dagger
DOI: 10.1023/B:JACO.0000023006.04375.60
Abstract
In this paper we prove that there are finitely many triangle-free distance-regular graphs with degree 8, 9 or 10.
Pages: 205–217
Keywords: distance-regular graphs; bannai-Itô conjecture
Full Text: PDF
References
1. E. Bannai and T. Ito, “The study of distance-regular graphs from the algebraic (i.e. character theoretical) viewpoint,” Proceedings of Symposia in Pure Mathematics 47 (1987), 343-349.
2. E. Bannai and T. Ito, “On distance-regular graphs with fixed valency,” Graphs and Combinatorics 3 (1987), 95-109.
3. E. Bannai and T. Ito, “On distance-regular graphs with fixed valency II,” Graphs and Combinatorics 4 (1988), 219-228.
4. E. Bannai and T. Ito, “On distance-regular graphs with fixed valency III,” Journal of Algebra 107 (1987), 43-52.
5. E. Bannai and T. Ito, “On distance-regular graphs with fixed valency IV,” European Journal of Combinatorics 10 (1989), 137-148.
6. A.E. Brouwer, A.M. Cohen, and A. Neumaier, Distance-Regular Graphs, Ergebnisse der Mathematik 3.18, Springer, Heidelberg, 1989.
7. J.H. Koolen and V. Moulton, “On a conjecture of Bannai and Ito: There are finitely many distance-regular graphs with degree 5, 6 or 7,” European Journal of Combinatorics 23 (2002), 987-1006.
8. P. Terwilliger, “Eigenvalue multiplicities of highly symmetric graphs,” Discrete Mathematics 41 (1982), 295- 302.
2. E. Bannai and T. Ito, “On distance-regular graphs with fixed valency,” Graphs and Combinatorics 3 (1987), 95-109.
3. E. Bannai and T. Ito, “On distance-regular graphs with fixed valency II,” Graphs and Combinatorics 4 (1988), 219-228.
4. E. Bannai and T. Ito, “On distance-regular graphs with fixed valency III,” Journal of Algebra 107 (1987), 43-52.
5. E. Bannai and T. Ito, “On distance-regular graphs with fixed valency IV,” European Journal of Combinatorics 10 (1989), 137-148.
6. A.E. Brouwer, A.M. Cohen, and A. Neumaier, Distance-Regular Graphs, Ergebnisse der Mathematik 3.18, Springer, Heidelberg, 1989.
7. J.H. Koolen and V. Moulton, “On a conjecture of Bannai and Ito: There are finitely many distance-regular graphs with degree 5, 6 or 7,” European Journal of Combinatorics 23 (2002), 987-1006.
8. P. Terwilliger, “Eigenvalue multiplicities of highly symmetric graphs,” Discrete Mathematics 41 (1982), 295- 302.