scholarly journals The Nonexistence of a Distance-Regular Graph with Intersection Array {22,16,5;1,2,20}

10.37236/5486 ◽  
2016 ◽  
Vol 23 (1) ◽  
Author(s):  
Supalak Sumalroj ◽  
Chalermpong Worawannotai
Keyword(s):  
Linear Space ◽  
Regular Graph ◽  
Intersection Array ◽  
Distance Regular Graph ◽  
Partial Linear Space ◽  
Combinatorial Properties ◽  
Local Graph ◽  
Partial Linear

We prove that a distance-regular graph with intersection array {22,16,5;1,2,20} does not exist. To prove this, we assume that such a graph exists and derive some combinatorial properties of its local graph. Then we construct a partial linear space from the local graph to display the contradiction.

scholarly journals Yet Another Distance Regular Graph Related to a Golay Code

10.37236/1220 ◽  
1995 ◽  
Vol 2 (1) ◽  
Author(s):  
Leonard H. Soicher
Keyword(s):  
Automorphism Group ◽  
Regular Graph ◽  
Intersection Array ◽  
Distance Regular Graph ◽  
Golay Code ◽  
Transitive Graph

We describe a new distance-regular, but not distance-transitive, graph. This graph has intersection array $\{110,81,12;1,18,90\}$, and automorphism group $M_{22}\colon 2$.

Sign in / Sign up

Export Citation Format

Share Document