[vA]ij= 
Möbius Graphs are kind of edge-weighted graphs in which at least one edge-weight is -1 [117-120]. They are used to represent the Möbius systems [121,373]. The vertex-adjacency matrix of Möbius graphs is symmetric V × V matrix:
[vA]ij= |
1 if the edge i - j is positively weighted |
| -1 if the edge i - j is negatively weighted | |
| 0 otherwise (11) |
In Figure 13, we give a five-membered Möbius cycle, denoted by MöG5. The corresponding vertex-adjacency matrix is given below the figure.
Figure 13. Labeled five-membered Möbius cycle.
vA(MöG5)= |
 |
0 |
1 |
0 |
0 |
1 |
 |
1 |
0 |
1 |
0 |
0 |
|||
0 |
1 |
0 |
-1 |
0 |
|||
0 |
0 |
-1 |
0 |
1 |
|||
1 |
0 |
0 |
1 |
0 |
