Geodesic
An eigenvalue characterization of antipodal distance-regular graphs
The electronic journal of combinatorics, Tome 4 (1997) no. 1
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Let $G$ be a regular (connected) graph with $n$ vertices and $d+1$ distinct eigenvalues. As a main result, it is shown that $G$ is an $r$-antipodal distance-regular graph if and only if the distance graph $G_d$ is constituted by disjoint copies of the complete graph $K_r$, with $r$ satisfying an expression in terms of $n$ and the distinct eigenvalues.
DOI : 10.37236/1315
Classification : 05C50, 05E30 
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     author = {M. A. Fiol},
     title = {An eigenvalue characterization of antipodal distance-regular graphs},
     journal = {The electronic journal of combinatorics},
     year = {1997},
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     number = {1},
     doi = {10.37236/1315},
     zbl = {0885.05082},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1315/}
}
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M. A. Fiol. An eigenvalue characterization of antipodal distance-regular graphs. The electronic journal of combinatorics, Tome 4 (1997) no. 1. doi: 10.37236/1315

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