[EC]ij= 
The edge-cycle incidence matrix of a polycyclic graph G, denoted by EC, is an E × Cn matrix (n being the size of the cycle), which is determined by the incidences of edges and cycles in G:
[EC]ij= |
1 if the i-th edge is incident with the j-th cycle |
| 0 otherwise (42) |
An example of a simple tricyclic graph is shown in Figure 26.
G15
Figure 26. A simple tricyclic graph.
The corresponding edge-cycle incidence matrix is given below:
C5 |
C6 |
C7 |
||||
EC(G15)= |
a |
 |
1 |
0 |
0 |
 |
b |
1 |
0 |
0 |
|||
c |
0 |
1 |
0 |
|||
d |
0 |
1 |
0 |
|||
e |
0 |
0 |
1 |
|||
f |
0 |
0 |
1 |
|||
g |
0 |
0 |
1 |
|||
h |
0 |
1 |
1 |
|||
i |
0 |
1 |
0 |
|||
j |
0 |
1 |
0 |
|||
k |
1 |
1 |
0 |
|||
l |
1 |
0 |
0 |
|||
m |
1 |
0 |
0 |
