journal article Nov 14, 1997

An Eigenvalue Characterization of Antipodal Distance-Regular Graphs

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.
Topics

No keywords indexed for this article. Browse by subject →

Cited By
11
On the k -independence number of graphs

A. Abiad, G. Coutinho · 2019

Discrete Mathematics
Linear Algebra and its Applications
Metrics
11
Citations
0
References
Details
Published
Nov 14, 1997
Vol/Issue
4(1)
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
Related

You May Also Like

The Sandwich Theorem

Donald E. Knuth · 1994

165 citations

Pólya's Permanent Problem

William McCuaig · 2004

81 citations

Distance-Regular Graphs

Edwin R. Van Dam, Jack H. Koolen · 2016

77 citations

A Dynamic Survey of Graph Labeling

Joseph A. Gallian · 2022

74 citations