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GENERALIZED ZAGREB INDEX OF GRAPHS
3.1.2 C C p,
) nanotubes and nanotori
( 4 8
q
A C 4C8
net is a trivalent decoration made by alternating C
4
and C
8
.
It can cover either a cylinder or a torus.
Let G = TURC C p,
) (R means rhomb, see Figure 3). We denote
4 8
( q
the number of rhombs in each row by p and the number of rhombs in each
column by q. Then V ( G)
= 4 pq , E ( G)
= p(6q
−1)
and we have:
r s s r
r s s r
M
{ r,
s}(
G)
= 4 p(2
3 + 2 3 ) + (6 pq − 5p)(3
3 + 3 3 ) =
r+
2 s s+
2 r
r+
s
p(2
3 + 2 3 + 2(6q
− 5)3 ) .
Figure 3. TURC C (8,4
4 8
)
Now, let T = TRC C p,
) be the nanotorus related to G. Then
( 4 8
q
V ( T ) = 4 pq , E( T ) = 6 pq and M .
r s s r
r+
s+
1
{ r,
s}
( T)
= 6 pq(3
3 + 3 3 ) = 4 pq3
Let G = TUSC C p,
) (S means square, see Fgure 4). We denote
4 8
( q
the number of squares in one row by p and the number of rows by
q ( q ≥ 2 ). Then V ( G)
= 4 pq , E ( G)
= p(6q
− 2)
and we have:
M
{ r,
s
r s s r r+
s
r+
s
}( G)
= 4 p(2
3 + 2 3 + 2 + (3q
− 4)3 ) .
Figure 4. TUSC 4
C 8
(4,8)
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