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

Table 5.

GFD values for reverse degree and reverse neighborhood degree of BRE(m, n, r) zeolite, when Inline graphic.

Inline graphic Reverse DegreeInline graphic Reverse Neighborhood DegreeInline graphic
q=2 q=3 q=4 q=5 q=6 q=2 q=3 q=4 q=5 q=6
Inline graphic m=n=r=2 13.551 13.264 13.077 12.939 12.831 29.76 29.102 28.615 28.237 27.934
m=n=r=3 11.837 11.051 10.55 10.207 9.9592 31.088 30.331 29.765 29.319 28.952
m=n=r=4 9.8182 8.7225 8.096 7.7019 7.4352 29.037 27.708 26.764 26.065 25.535
m=n=r=5 8.2605 7.0932 6.484 6.1246 5.8928 26.58 24.52 23.077 22.069 21.354
m=n=r=6 7.0914 5.9486 5.3911 5.0759 4.8781 24.211 21.581 19.912 18.855 18.157
Inline graphic m=n=r=2 13.262 12.881 12.614 12.405 12.234 27.366 26.403 25.708 25.166 24.729
m=n=r=3 13.65 13.368 13.179 13.034 12.918 30.337 29.415 28.732 28.205 27.786
m=n=r=4 12.407 11.658 11.13 10.746 10.46 30.181 29.177 28.474 27.97 27.597
m=n=r=5 10.991 9.9116 9.2352 8.7938 8.4916 29.48 28.357 27.535 26.901 26.399
m=n=r=6 9.7398 8.5112 7.8158 7.3932 7.1173 28.667 27.429 26.5 25.762 25.166
HM(BRE) m=n=r=2 13.452 13.085 12.845 12.671 12.535 27.91 27.006 26.32 25.766 25.311
m=n=r=3 13.778 13.454 13.229 13.058 12.922 30.62 29.822 29.237 28.78 28.41
m=n=r=4 12.668 11.968 11.49 11.151 10.901 30.256 29.333 28.714 28.284 27.973
m=n=r=5 11.363 10.352 9.7167 9.2955 9.0011 29.462 28.408 27.686 27.16 26.76
m=n=r=6 10.174 8.9949 8.3131 7.8887 7.6058 28.642 27.501 26.712 26.122 25.657
R(BRE) m=n=r=2 9.9439 9.0493 8.5148 8.1603 7.9096 24.617 23.212 22.443 21.964 21.633
m=n=r=3 6.5972 5.5973 5.0948 4.8037 4.6185 16.192 14.175 13.185 12.596 12.203
m=n=r=4 4.8923 4.0155 3.615 3.3965 3.262 11.552 9.6746 8.8033 8.3078 7.9922
m=n=r=5 3.8813 3.125 2.7998 2.6276 2.5228 8.9055 7.2622 6.5428 6.1512 5.909
m=n=r=6 3.2148 2.5562 2.2844 2.1428 2.0573 7.2252 5.7937 5.1946 4.8769 4.683
H(BRE) m=n=r=2 9.7998 8.8714 8.3132 7.9453 7.6881 24.355 22.853 22.033 21.522 21.167
m=n=r=3 6.3984 5.3948 4.8982 4.6142 4.4349 15.738 13.714 12.72 12.127 11.732
m=n=r=4 4.7073 3.8441 3.4559 3.2458 3.117 11.089 9.2406 8.3901 7.9104 7.6068
m=n=r=5 3.7176 2.9809 2.6684 2.5038 2.4039 8.4896 6.894 6.2027 5.829 5.5987
m=n=r=6 3.0703 2.433 2.1729 2.0381 1.9567 6.8584 5.4806 4.9096 4.6083 4.4249
GA(BRE) m=n=r=2 12.155 11.593 11.223 10.956 10.75 29.184 28.107 27.266 26.616 26.113
m=n=r=3 8.8522 7.7681 7.1663 6.7955 6.5492 24.477 22.202 20.929 20.148 19.625
m=n=r=4 6.7495 5.6748 5.1472 4.8473 4.6586 19.064 16.374 15.026 14.24 13.73
m=n=r=5 5.4235 4.449 4.0048 3.7628 3.6138 15.321 12.716 11.513 10.845 10.425
m=n=r=6 4.5248 3.6531 3.2753 3.0744 2.952 12.727 10.339 9.2984 8.7384 8.3936
Inline graphic m=n=r=2 13.447 13.205 13.058 12.955 12.877 29.359 28.608 28.059 27.636 27.293
m=n=r=3 11.581 10.74 10.185 9.7994 9.52 31.066 30.304 29.748 29.318 28.971
m=n=r=4 9.4279 8.2774 7.6283 7.2292 6.9653 28.842 27.313 26.189 25.351 24.719
m=n=r=5 7.8266 6.6406 6.0381 5.6912 5.4714 26.035 23.619 21.987 20.904 20.167
m=n=r=6 6.656 5.5224 4.9855 4.6881 4.5036 23.369 20.421 18.676 17.627 16.953
Inline graphic m=n=r=2 12.155 11.604 11.283 11.073 10.926 25.407 24.305 23.48 22.813 22.267
m=n=r=3 13.857 13.605 13.447 13.336 13.253 27.996 26.699 25.728 24.986 24.418
m=n=r=4 14.046 13.852 13.74 13.664 13.608 27.827 26.455 25.567 24.965 24.538
m=n=r=5 13.562 13.148 12.839 12.592 12.388 27.039 25.352 24.205 23.381 22.766
m=n=r=6 12.811 12.097 11.567 11.167 10.863 26.138 24.085 22.652 21.639 20.915