Hyper- and reverse-Wiener indices of F-sums of graphs
The Wiener index W ( G ) = ∑ { u , v } ⊂ V ( G ) d ( u , v ) , the hyper-Wiener index W W ( G ) = 1 2 ∑ { u , v } ⊂ V ( G ) [ d ( u , v ) + d 2 ( u , v ) ] and the reverse-Wiener index Λ ( G ) = n ( n − 1 ) D 2 − W ( G ) , where d ( u , v ) is the distance of two vertices u , v in G , d 2 ( u , v )...
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| Veröffentlicht in: | Discrete Applied Mathematics 2010-07, Vol.158 (13), p.1433-1440 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | The Wiener index
W
(
G
)
=
∑
{
u
,
v
}
⊂
V
(
G
)
d
(
u
,
v
)
, the hyper-Wiener index
W
W
(
G
)
=
1
2
∑
{
u
,
v
}
⊂
V
(
G
)
[
d
(
u
,
v
)
+
d
2
(
u
,
v
)
]
and the reverse-Wiener index
Λ
(
G
)
=
n
(
n
−
1
)
D
2
−
W
(
G
)
, where
d
(
u
,
v
)
is the distance of two vertices
u
,
v
in
G
,
d
2
(
u
,
v
)
=
d
(
u
,
v
)
2
,
n
=
|
V
(
G
)
|
and
D
is the diameter of
G
. In [M. Eliasi, B. Taeri, Four new sums of graphs and their Wiener indices, Discrete Appl. Math. 157 (2009) 794–803], Eliasi and Taeri introduced the F-sums of two connected graphs. In this paper, we determine the hyper- and reverse-Wiener indices of the F-sum graphs and, subject to some condition, we present some exact expressions of the reverse-Wiener indices of the F-sum graphs. |
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| ISSN: | 0166-218X 1872-6771 |
| DOI: | 10.1016/j.dam.2010.04.003 |