GRAPH THEORETICAL MATRICES in CHEMISTRY
Contents
2. THE ADJANCENCY MATRIX and RELATED MATRICES
1. The Vertex-Adjacency Matrix of Simple Graphs
2. The Linear Representation of the Vertex-Adjacency Matrix of Acyclic Structures
3. The Vertex-Adjacency Matrix of Multiple Graphs
4. The Atom-Conectivity Matrix
5. The Edge-Adjacency Matrix
6. The Vertex-Adjacency Matrix of Weighted Graphs
7. The Vertex-Adjacency Matrix of Möbius Graphs
8. The Augmented Vertex-Adjacency Matrix
9. The Edge-Weighted Edge-Adjacency Matrix
10. The Vertex-Connectivity Matrix
11. The Edge-Connectivity Matrix
12. Extended Adjacency Matrices
13. Zagreb Matrices
14. The Hückel Matrix
15. The Laplacian Matrix
16. The Generalized Laplacian Matrix
17. The Augmented Vertex-Degree Matrix
1. The Vertex-Edge Incidence Matrix
2. The Edge-Vertex Incidence Matrix
3. The Edge-Cycle Incidence Matrix
4. The Cycle-Edge Incidence Matrix
5. The Vertex-Path Incidence Matrix
6. The Weighted-Hexagon-Kekulé-Structure Incidence Matrix
4. DISTANCE MATRIX and RELATED MATRICES
1. The Standard or Vertex-Distance Matrix
2. The Vertex-Distance-Path Matrix
3. The Reciprocal Vertex-Distance-Path-Matrix
4. The Vertex-Distance-Delta Matrix
5. The Edge-Distance Matrix
6. The Vertex-Distance-Complement Matrix
7. The Augmented Vertex-Distance Matrix
8. The Edge-Weighted Vertex-Distance Matrix
9. The Barysz Vertex-Distance Matrix
10. The Complement of the Barysz Vertex-Distance Matrix
11. The Reciprocal Barysz Vertex-Distance Matrix
12. The Reciprocal of the Complement of the Barysz Vertex-Distance Matrix
13. The Complementary Vertex-Distance Matrix
14. The Reciprocal of the Complementary Vertex-Distance Matrix
15. The Detour Matrix
16. The Detour-Path Matrix
17. The Detour-Delta Matrix
18. The Edge-Weighted Detour Matrix
19. The Maximum-Minimum Path Matrix
20. The Detour-Complement Matrix
21. The Vertex-Distance Matrix and the Detour Matrix of Complete Graphs and Complete Bipartite Graphs
22. The Vertex-Harary Matrix
23. The Edge-Harary Matrix
24. The Edge-Weighted-Harary Matrix
25. The Modified Edge-Harary Matrix
26. The Distance-Degree Matrices
27. The Resistance-Distance Matrix
28. Distance/Distance Matrices
1. Adjacency-Plus-Distance Matrices
2. The Distance-Sum-Connectivity Matrix
3. Wiener Matrices
4. The Modified Edge-Wiener Matrix
5. The Reverse Wiener Matrix
6. The Reverse-Detour Matrix
7. Szeged Matrices
8. Reciprocal Szeged Matrices
9. The Unsymmetric Szeged Matrix
10. Cluj Matrices
11. Reciprocal Cluj Matrices
12. The Hosoya Matrix
13. The Path Matrix
14. The All-Path Matrix
15. The Expanded Vertex-Distance Matrix
16. The Quotient Matrices
17. The Random-Walk Markov Matrix
18. The Transfer Matrix
1. Construction of Graphical Matrices
2. Numerical Realization of Graphical Matrices
2.1. Use of the Randic Connectivity index
2.2. Use of the Hosoya Index
3. Generalized Method for Constructing Graphical Matrices and for Getting Their Numerical Representations