%0 Journal Article %1 godsil88 %A Godsil, Chris D. %D 1988 %I Springer-Verlag %J Combinatorica %K diameter distance-regular graph.theory %N 4 %P 333--343 %R 10.1007/BF02189090 %T Bounding the Diameter of Distance-Regular Graphs %V 8 %X Let $G$ be a connected distance-regular graph with valency $k>2$ and diameter $d$, but not a complete multipartite graph. Suppose that $þeta$ is an eigenvalue of $G$ with multiplicity $m$ and that $k$. We prove that both $d$ and $k$ are bounded by functions of $m$. This implies that, if $m>1$ is given, there are only finitely many connected, co-connected distance-regular graphs with an eigenvalue of multiplicity $m$.

@article{godsil88, abstract = {Let $G$ be a connected distance-regular graph with valency $k>2$ and diameter $d$, but not a complete multipartite graph. Suppose that $\theta$ is an eigenvalue of $G$ with multiplicity $m$ and that $\theta \neq \pm k$. We prove that both $d$ and $k$ are bounded by functions of $m$. This implies that, if $m>1$ is given, there are only finitely many connected, co-connected distance-regular graphs with an eigenvalue of multiplicity $m$.}, added-at = {2014-01-05T01:17:29.000+0100}, author = {Godsil, Chris D.}, biburl = {https://www.bibsonomy.org/bibtex/26c2e25493464fb2fa2c7bfd7f0d14973/ytyoun}, doi = {10.1007/BF02189090}, interhash = {6ca0fb286bb76a84ca97d93c259a052e}, intrahash = {6c2e25493464fb2fa2c7bfd7f0d14973}, issn = {0209-9683}, journal = {Combinatorica}, keywords = {diameter distance-regular graph.theory}, language = {English}, number = 4, pages = {333--343}, publisher = {Springer-Verlag}, timestamp = {2017-11-22T02:22:16.000+0100}, title = {Bounding the Diameter of Distance-Regular Graphs}, volume = 8, year = 1988 }