ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 01 Apr 2019 22:39:31 +0200What are distance regular graphshttps://ask.sagemath.org/question/45960/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}.Sun, 31 Mar 2019 16:09:05 +0200https://ask.sagemath.org/question/45960/what-are-distance-regular-graphs/Comment by slelievre for <p>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</p>
<p>{b0,b1,...,bD−1;c1,c2,...,cD}.</p>
https://ask.sagemath.org/question/45960/what-are-distance-regular-graphs/?comment=45980#post-id-45980Welcome to Ask Sage. Thank you for your post. What is your question?Mon, 01 Apr 2019 22:39:31 +0200https://ask.sagemath.org/question/45960/what-are-distance-regular-graphs/?comment=45980#post-id-45980