An  Eigenvalue Characterization   of Antipodal Distance-Regular Graphs

M. A. Fiol

doi:10.37236/1315

journal article Nov 14, 1997

An Eigenvalue Characterization of Antipodal Distance-Regular Graphs

M. A. Fiol

The Electronic Journal of Combinatorics Vol. 4 No. 1 · The Electronic Journal of Combinatorics

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Abstract

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.

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Published: Nov 14, 1997
Vol/Issue: 4(1)

Authors

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M. A. Fiol

Cite This Article

M. A. Fiol (1997). An Eigenvalue Characterization of Antipodal Distance-Regular Graphs. The Electronic Journal of Combinatorics, 4(1). https://doi.org/10.37236/1315

An Eigenvalue Characterization of Antipodal Distance-Regular Graphs

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