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GENERALIZED ZAGREB INDEX OF GRAPHS
1
Nanotube G M
1( G)
= M
{1,0}
( G)
M
2
( G)
= M
{1,1 }(
G)
2
TUSC C p,
)
4p(9q-5) 2p(27q-20)
4 8
( q
TUHC
5C7 (2 p,
q)
4p(36q-1) 6p(36q-5)
TUVC (2 5C7 p,
q)
6p(24q-5) 2p(108q-31)
TUSC C ( p,
)
2p(36q-19) 4p(27q-17)
5 7
q
5 7
q
5C7
( p,
q
5 6 7
q
5C6C7
( p,
q
TUHAC C ( p,
) 2p(36q-5) 3p(36q-7)
TUVAC ) 6q(12p-5) q(108p-61)
TUHAC C C ( p,
) 4p(36q-5) 6p(36q-7)
TUVAC ) 2q(72p-25) q(216p-85)
Table 2. First and second Zagreb indices of some nanotori
1
Nanotorus T M
1( T ) = M
{1,0}
( G)
M
2
( T ) = M
{1,1 }(
G)
2
TZC
6
( p,
q)
18 pq
27 pq
TAC ( p,
)
6
q
TRC
4C8 ( p,
q)
TSC C p,
)
( 4 8
q
THC
5C7(2
p,
q)
TVC (2 5C7 p,
q)
TSC C ( p,
)
5 7
q
THAC
5C7
( p,
q)
TVAC C ( p,
)
5 7
q
THAC
5C6C7
( p,
q)
TVAC C C ( p,
)
5 6 7
q
36 pq
54 pq
144 pq
216 pq
72 pq
108 pq
144 pq
216 pq
CONCLUSIONS
The generalized Zagreb index was defined and next formulas for
calculating this new topological index in some nanotubes and nanotori
were derived. The classical Zagreb indices formulas for the considered
nanotubes and nanotori were tabulated.
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