On Distance in Some Finite Planes and Graphs Arising from Those Planes

Table 2

Circles with centre C and radius r of the projective plane of order 3.

C	r = 1	r = 2	r = 3
00	{01, 10, 11, 12}	{02, 20, 21, 22}	{(0), (1), (2), (ꝏ)}
01	{10, 11, 12, 00, 02}	{22, 21, 20, (ꝏ)}	{(0), (1), (2)}
02	{01, 12, 11, 10, (ꝏ)}	{00, 22, 21, 20}	{(0), (1), (2)}
10	{00, 01, 02, 20, 21, 22, 11}	{12, (0), (1), (2)}	{(ꝏ)}
11	{02, 01, 00, 22, 21, 20, 12, 10}	{(0), (1), (2), (ꝏ)}	{}
12	{02, 01, 00, 22, 21, 20, 11, (ꝏ)}	{10, (0), (1), (2)}	{}
20	{10, 11, 12, 21, (0), (1), (2)}	{00, 01, 02, 22}	{(ꝏ)}
21	{12, 11, 10, 22, 20, (0), (1), (2)}	{02, 01, 00, (ꝏ)}	{}
22	{12, 11, 10, 21, (0), (1), (2), (ꝏ)}	{02, 01, 00, 20}	{}
(0)	{20, 21, 22, (1)}	{10, 11, 12, (2)}	{00, 01, 02, (ꝏ)}
(1)	{20, 21, 22, (0), (2)}	{10, 11, 12, (ꝏ)}	{00, 01, 02}
(2)	{20, 21, 22, (1), (ꝏ)}	{10, 11, 12, (0)}	{00, 01, 02}
(ꝏ)	{02, 12, 22, (2)}	{01, 11, 21, (1)}	{00, 10, 20, (0)}