Chemistry Reference
In-Depth Information
Fig. 7.23
The unicyclic
graph
C
(2,4, 3)
Fig. 7.24
The tree
P
(2,4, 3)
of
B
d
,
k
. So we can apply the Corollaries 7.2.3 and 7.2.5 and then Corollary 7.5.19,
to get the formulae for the first and second Zagreb indices of the tree
P
(
d
,
k
,
n
).
Corollary 7.5.21
The first and second Zagreb indices of
P
(
d
,
k
,
n
) are given by:
s
=
0
d
s
,
1)
2
k
−
3
nd
2
nd
k
−
1
1.
M
1
(
P
(
d
,
k
,
n
))
=
4
d
(
n
−
1)
+
4
n
−
6
+
+
+
nd
(
d
+
k
−
s
=
0
d
s
,
and
3
3
d
2
4
d
2
(
d
2.
M
2
(
P
(
d
,
k
, 2))
=
+
4
d
+
1
+
+
1)
⎧
⎨
⎩
(2
n
−
1)
d
2
+
6
nd
+
4
n
−
8
d
−
8
if k
=
2
M
2
(
P
(
d
,
k
,
n
))
=
.
s
=
0
d
s
k
−
3
1)
2
2
nd
2
(
d
3(
n
−
1)(
d
+
+
n
−
2
d
−
5
+
+
1)
if k
≥
3
Our last examples are about dendrimer trees and a class of dendrimer graphs. Den-
drimers are hyperbranched molecules, synthesized by repeatable steps, either by
