Skip to main content
. 2026 Apr 6;16:11641. doi: 10.1038/s41598-026-45013-2

Table 3.

Edge partition of BRE(m, n, r) with Inline graphic based on reverse neighborhood degree Inline graphic.

Inline graphic Inline graphic Frequency Inline graphic Inline graphic Frequency
(6,8) (9,11) 2 (10,14) (3,7) 2(m+n+r-3)
(6,9) (8,11) 2m (10,15) (2,7) 2(2mr-2m-3r+5)
(6,10) (7,11) 2(m-1) (11,11) (6,6) 2(m-2)(n-2)
(7,8) (9,10) 2 (11,13) (4,6) 2(2n-1)
(7,9) (8,10) 2(m+r-3) (11,14) (3,6) 2(2mn-3n+2)
(7,10) (7,10) 2(m-1)(r-2) (11,15) (2,6) 2(2mn-4m+n+2r-5)
(7,13) (4,10) 2(r-1) (12,13) (4,5) 2(r-2)
(7,14) (3,10) 2(m-1)(r-1) (12,14) (3,5) 2(r-2)
(8,10) (7,9) 4 (12,15) (2,5) 2(r-2)(3n-5)
(8,11) (6,9) 4 (13,14) (3,4) 2(r-1)
(9,9) (8,8) 2 (13,16) (1,4) 2(n+r-2)
(9,10) (7,8) 2m (14,14) (3,3) 2(m-1)
(9,11) (6,8) 2(m+r-2) (14,15) (2,3) 2(mn+mr-m-1)
(9,14) (3,8) 2(m-1) (14,16) (1,3) 2(mn+2mr-2m-2n-2r+3)
(9,15) (2,8) 2(m+r-2) (15,15) (2,2) 2mn+mr+4nr-2m-6n-3r+4
(10,10) (7,7) 6 (15,16) (1,2) 2(3mn+4mr+5nr-12m-9n-12r+21)
(10,11) (6,7) 2(m+4n-10) (16,16) (1,1) 16mnr-24mn-22mr-21nr+34m+30n+29r-42
(10,13) (4,7) 2(n-1)