TITLE: Does there exist a regular graph of degree 4, diameter 3, 32 vertices?
QUESTION [6 upvotes]: Does there exist a regular graph of degree 4 having its diameter equal to three and its number of vertices equal to 32? What I know is http://www-ma4.upc.es/~comellas/delta-d/desc_g/desc_g3.html
( the second graph).

REPLY [9 votes]: Here's an adjacency list, it's 4-regular, so there should be 4 vertices per line.   I'm sure it will be easier for you to get the graph that for me to figure out the software interface here.
14    3    9   24
 5    8   25    3
30   16   21    7
 1    0   29   30
15   28   23   11
28   16   26    1
31   19   10   23
20   27    2   29
15   14    1   22
 0   13   17   28
 6   21   22   25
17   13   18    4
20   24   26   22
 9   11   25   20
 8    0   31   19
21    4    8   24
 5   31   20    2
 9   11   30   27
31   11   26   30
 6   28   14   27
13   16   12    7
10   24    2   15
12   10    8   27
26   29    4    6
12   21    0   15
10   13    1   29
12    5   23   18
19   17    7   22
 5   19    4    9
23    3    7   25
17    2    3   18
16   18    6   14

There appear to be many such graphs.

(Added by J.O'Rourke).
Here is the graph above, but with vertices labeled from $1$ to $32$ rather than $0$ to $31$: