THE NON-ISOLATED DOMINATION NUMBER OF GRAPHS
A subset S of the vertex set V (G) of a graph G is said to be dominating set if every vertex not in S is adjacent to at least one vertex in S. In this research, we introduce a new domination parameter, called the non-isolated domination number of a graph. A subset S of V of a nontrivial graph G i...
Saved in:
| Main Author: | |
|---|---|
| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/42231 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | A subset S of the vertex set V (G) of a graph G is said to be dominating set if
every vertex not in S is adjacent to at least one vertex in S. In this research,
we introduce a new domination parameter, called the non-isolated domination
number of a graph. A subset S of V of a nontrivial graph G is said to be non-
isolated dominating set, if S is a dominating set and there are no zero degree
vertex in subgraph induced by S. The minimum cardinality taken over all non-
isolated dominating sets is called the non-isolated domination number and is
denoted by
I . In this research, we obtained the best lower and upper bounds of
the non-isolated domination number of a connected graph. We also determine
the characterization of connected graphs that have the non-isolated domination
number 2. Furthermore, we determine the non-isolated domination number of
complete, complete n-partite, wheel, fan, star, cycle, and path graphs. We also
determine the relationship between the non- isolated domination number and
diameter of tree graphs and we also give the characterization of tree graphs
that have the non-isolated domination number 2
. |
|---|