2019-04-01 22:38:18 +0200 | asked a question | What are distance regular graphs A connected graph Γ with diameter D is called distance-regular if there are constants ci,ai,bi — the so-called intersection numbers — such that for all i = 0,1,...,D, and all vertices x and y at distance i = d(x,y), among the neighbors ofy, there are ci at distance i−1 from x, ai at distance i, and bi at distance i+1. It follows that Γ is a regular graph with valency k = b0, and that ci +ai +bi = kfor all i = 0, 1, . . . , D. By these equations, the intersection numbers ai can be expressed in terms of the others, and it is standard to put these others in the so-called intersection array {b0,b1,...,bD−1;c1,c2,...,cD}. |

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.