View source for Regular graph

{{TEX|done}}{{MSC|05C99}}

An unoriented [[graph]] in which each vertex has the same degree.  If the common degree is $k$, the graph may be termed ''$k$-regular''.

A '''strongly regular graph''' is a regular graph in which any two adjacent vertices have the same number of neighbours in common, and any two non-adjacent vertices have the same number of neighbours in common.  The [[Graph complement|complement]] of a strongly regular graph is again strongly regular.

A '''distance regular graph''' is one with the property that for any two vertices $x,y$ the number of vertices at distance $i$ from $x$ and $j$ from $y$ depends only on $i$, $j$ and the distance $d(x,y)$.

====References====
* Richard A Brualdi, Herbert J. Ryser, "Combinatorial matrix theory", Cambridge University Press (2014) ISBN 978-0-521-32265-2  {{ZBL|0746.05002}} {{ZBL|1286.05001}}
* Andries E. Brouwer, Arjeh M. Cohen, Arnold Neumaier, "Distance-regular graphs" Springer (1989) ISBN 3-642-74343-6 {{ZBL|0747.05073}}