Table 5 GFD values for reverse degree and reverse neighborhood degree of BRE(m, n, r) zeolite, when \(m=n=r\).

From: GFD analysis for BRE zeolite graph through reverse degree and reverse neighborhood degree based topological descriptors

\(D_q^{\varphi }(BRE(m,n,r))\)

Reverse Degree\((\mathfrak {R}d)\)

Reverse Neighborhood Degree\((\mathfrak {R}Nd)\)

q=2

q=3

q=4

q=5

q=6

q=2

q=3

q=4

q=5

q=6

\(M_1(BRE)\)

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

\(M_2(BRE)\)

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

\(ReZG_2(BRE)\)

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

\(ReZG_3(BRE)\)

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

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