chemia - Studia

MAHDIEH AZARI, ALI IRANMANESH, ABOLFAZL TEHRANIAN
192
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
)
(
2
2
1
1
2
)
(
)
(
2
G
V
G
V
G
E
B ,
2
)
(
2
1
2
2
)
(
2 ⎟ ⎟ ⎠
⎞
⎜
⎜
⎝
⎛
=
G
V
G
E
B ,
) )
(
2
)
(
(
)
(
1)
)
(
(
)
( 1
1
1
)
(
2
2
2
)
( 2
2
3
2
4
2
1
1
1
G
E
G
M
G
V
G
V
G
V
B
G
V
G
V
u
u
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
= ∑
∈
δ
Afterwards, we find
∑
∈ 5
4
3
}
,
{
2
1
0 )
]
[
,
(
B
B
B
f
e
G
G
f
e
d
U
U
. By Proposition 2.2, we have:
=
∑
}∈ 3
,
{
2
1
0 )
]
[
,
(
B
f
e
G
G
f
e
d
=
=
=
∈
∑ )]}
,
),(
,
[(
)],
,
),(
,
[(
,
}
,
) :{
]
,
],[
,
([
{ 2
1
2
1
2
1
2
1
3
1
1
1
1
1
0 z
z
u
u
f
v
v
u
u
e
B
f
e
G
z
u
v
u
d
=
∑
∑
∈
⊆
)
( )
(
]}
,
],[
,
{[
1
1
1
1
1
0
3
2
1
1 1
1
1
1
1
)
]
,
],[
,
([
)
(
G
V
u
G
E
z
u
v
u
G
z
u
v
u
d
G
V
∑
∑
∈
∈
∈
)
(
]
,
[
)
(
]
,
[
},
,
{
1
1
1
1
1
0
3
2
1
1
1
1
1
1
1
1
1
)
]
,
],[
,
([
)
(
2
1
G
E
v
u
G
E
t
z
v
u
z
G
t
z
v
u
d
G
V ,
=
∑
}∈ 4
,
{
2
1
0 )
]
[
,
(
B
f
e
G
G
f
e
d
=
=
=
∈
+
∑ )]}
,
),(
,
[(
)],
,
),(
,
[(
,
}
,
1:{
)
]
,
],[
,
([
{ 2
1
2
1
2
1
2
1
4
1
1
1
1
1
0 z
z
t
u
f
v
v
u
u
e
B
f
e
G
z
u
v
u
d
=
+
− ∑ ∑
∈
⊆
4
)
( )
(
]}
,
],[
,
{[
1
1
1
1
1
0
3
2
4
2
1
1 1
1
1
1
1
)
]
,
],[
,
([
)
)
(
)
(
( B
G
z
u
v
u
d
G
V
G
V
G
V
u
G
E
z
u
v
u
4
)
(
]
,
[
)
(
]
,
[
},
,
{
1
1
1
1
1
0
3
2
4
2
1
1
1
1
1
1
1
1
1
)
]
,
],[
,
([
)
)
(
)
(
(
2
1
B
G
t
z
v
u
d
G
V
G
V
G
E
v
u
G
E
t
z
v
u
z
+
− ∑ ∑
∈
∈
∈
,
=
∑
}∈ 5
,
{
2
1
0 )
]
[
,
(
B
f
e
G
G
f
e
d
=
=
=
∈
∑ )]}
,
),(
,
[(
)],
,
),(
,
[(
,
}
,
:{
)
]
,
],[
,
([
{ 2
1
2
1
2
1
2
1
5
1
1
1
1
1
0 t
t
z
z
f
v
v
u
u
e
B
f
e
G
t
z
v
u
d
[ ]
{ }
∑
∑
∉
∈
∈
1
1
1
1
1
1
1
1
1
1
,
,
),
(
]
,
[
1
1
1
1
1
0
)
(
,
4
2 )
]
,
],[
,
([
)
(
2
1
v
u
t
z
G
E
t
z
G
E
v
u
G
t
z
v
u
d
G
V .
Based on the above computations and since each pair of )
5
1
( ≤
≤ i
B i is
disjoint, we have:
=
∑
∈ 5
4
3
}
,
{
2
1
0 )
]
[
,
(
B
B
B
f
e
G
G
f
e
d
U
U
=
∑∑
= ∈
5
3 }
,
{
2
1
0 )
]
[
,
(
i
B
f
e
i
G
G
f
e
d
[ ] { }
[ ]
+
∑
∑
∈
∈
∈
)
(
,
,
,
1
1
1
1
1
0
)
(
,
3
2
1
1
1
1
1
1
1
1
1
)
]
,
],[
,
([
)
(
2
1
G
E
t
z
v
u
z
G
E
v
u
G
t
z
v
u
d
G
V