scholarly journals A characterization of Q-polynomial distance-regular graphs

2008 ◽  
Vol 308 (14) ◽  
pp. 3090-3096 ◽  
Author(s):  
Arlene A. Pascasio
Keyword(s):  
Regular Graphs ◽  
Distance Regular Graphs

Characterization of certain distance-regular graphs by forbidden subgraphs

2007 ◽  
Vol 75 (3) ◽  
pp. 420-423 ◽  
Author(s):  
V. V. Kabanov ◽  
A. A. Makhnev ◽  
D. V. Paduchikh
Keyword(s):  
Regular Graphs ◽  
Forbidden Subgraphs ◽  
Distance Regular Graphs

scholarly journals A Short Proof of the Odd-Girth Theorem

10.37236/2289 ◽  
2012 ◽  
Vol 19 (3) ◽  
Author(s):  
Edwin R. Van Dam ◽  
Miquel Angel Fiol
Keyword(s):  
Connected Graph ◽  
Short Proof ◽  
Direct Proof ◽  
Regular Graphs ◽  
Distance Regular Graphs

Recently, it has been shown that a connected graph $\Gamma$ with $d+1$ distinct eigenvalues and odd-girth $2d+1$ is distance-regular. The proof of this result was based on the spectral excess theorem. In this note we present an alternative and more direct proof which does not rely on the spectral excess theorem, but on a known characterization of distance regular graphs in terms of the predistance polynomial of degree $d$.

scholarly journals A characterization of bipartite distance-regular graphs

2014 ◽  
Vol 446 ◽  
pp. 91-103 ◽  
Author(s):  
Guang-Siang Lee ◽  
Chih-wen Weng
Keyword(s):  
Regular Graphs ◽  
Distance Regular Graphs

scholarly journals An Eigenvalue Characterization of Antipodal Distance-Regular Graphs

10.37236/1315 ◽  
1997 ◽  
Vol 4 (1) ◽  
Author(s):  
M. A. Fiol
Keyword(s):  
Regular Graph ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Graph ◽  
Regular Graphs ◽  
Distance Regular Graph ◽  
Distance Regular Graphs

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.

scholarly journals Quasi-Spectral Characterization of Strongly Distance-Regular Graphs

10.37236/1529 ◽  
2000 ◽  
Vol 7 (1) ◽  
Author(s):  
M. A. Fiol
Keyword(s):  
Harmonic Mean ◽  
Spectral Characterization ◽  
Strongly Regular Graphs ◽  
Regular Graphs ◽  
Strongly Regular ◽  
Distance Regular Graphs

A graph $\Gamma$ with diameter $d$ is strongly distance-regular if $\Gamma$ is distance-regular and its distance-$d$ graph $\Gamma _d$ is strongly regular. The known examples are all the connected strongly regular graphs (i.e. $d=2$), all the antipodal distance-regular graphs, and some distance-regular graphs with diameter $d=3$. The main result in this paper is a characterization of these graphs (among regular graphs with $d$ distinct eigenvalues), in terms of the eigenvalues, the sum of the multiplicities corresponding to the eigenvalues with (non-zero) even subindex, and the harmonic mean of the degrees of the distance-$d$ graph.

Sign in / Sign up

Export Citation Format

Share Document