[CE]ij= 
The cycle-edge incidence matrix of a polycyclic graph G, denoted by CE, is an Cn× E matrix, which is determined by the incidences of cycles and edges in G:
[CE]ij= |
1 if the i-th cycle is incident with the j-th edge |
| 0 otherwise (43) |
It is evident that the cycle-edge incidence matrix is the transpose of the edge-cycle incidence matrix. This matrix presented because it is used in the counting formula of spanning trees of graphs (see section 2.15).
The CE matrix of G15 is given below:
a |
b |
c |
d |
e |
f |
g |
h |
i |
j |
k |
l |
m |
||||
CE(G15)= |
C5 |  |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
 |
| C6 | 0 |
0 |
1 |
1 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
0 |
|||
| C7 | 0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
