International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 03 Issue: 04 | Mar 16 www.irjet.net p-ISSN: 2395-0072
© 2016, IRJET | Impact Factor value: 4.45 | ISO 9001:2008 Certified Journal | Page 1548
Split and Non Split Neighborhood Connected Domination in Fuzzy Graphs
C.V.R.Harinarayanan
1
, S.Geetha
2
1
Assistant Professor, Department of Mathematics, Govt.Arts College, Paramakudi, India
2
Assistant Professor, Department of Mathematics,Kings College of Engg., Tamilnadu, India
---------------------------------------------------------------------***---------------------------------------------------------------------
Abstract - Let G be a connected fuzzy graph without
isolated vertices. A dominating set D of G is said to be
neighborhood connected dominating set if the induced
subgraph D N is connected. A neighborhood
connected dominating set D of G is a split neighborhood
connected dominating set D if the induced subgraph
D V is disconnected. The split neighborhood
connected domination number G
snc
of G is the
minimum cardinality of a split neighborhood connected
dominating set. A neighborhood connected dominating set
D of G is a nonsplit neighborhood connected dominating
set D if the induced subgraph D V is connected. The
nonsplit neighborhood connected domination number
G
nsnc
of G is the minimum cardinality of a non split
neighborhood connected dominating set. In this paper we
study these parameters. Also we present some bounds on
these parameters.
Key Words: : neighborhood connected dominating set
,split neighborhood connected dominating set, nonsplit
neighborhood connected dominating set.
1.INTRODUCTION:A fuzzy graph , G is a set
with a pair of relations
v u v u that such V V and V , 1 , 0 : 1 , 0 :
for all V v u , .
A non empty set V D of a fuzzy graph , G is
a dominating set of G if every vertex in V-D is adjacent to
some vertex in D .The domination number G is the
minimum cardinality taken over all the minimal
dominating sets of G.
The order of a fuzzy graph G is O (G)=
V u
u
The size of a fuzzy graph G is S (G)=
E uv
uv
A dominating set of a fuzzy graph G is a split (non split)
dominating set if the induced subgraph D V is
disconnected (connected).
The split (non split) domination number G G
ns s
is
the minimum cardinality of a split(non split) dominating
set.
Two nodes that are joined by a path are said to be
connected.
A fuzzy graph G is said to be connected if any two nodes
are connected.
Let G be a connected fuzzy graph without isolated vertices.
A dominating set D of G is said to be neighborhood
connected dominating set if the induced subgraph
D N is connected
A neighborhood connected dominating set D of G is a split
neighborhood connected dominating set D if the induced
subgraph D V is disconnected.
A neighborhood connected dominating set D of G is a
nonsplit neighborhood connected dominating set D if the
induced subgraph D V is connected.
Example:
4 . 0 1 . 0 1 . 0 , 2 . 0 d c b a
Neighborhood connected dominating set D ={b,d}
D N is connected.
b
d
c
a