- 464 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
Fundamentals of Domination in Graphs
About this book
"Provides the first comprehensive treatment of theoretical, algorithmic, and application aspects of domination in graphs-discussing fundamental results and major research accomplishments in an easy-to-understand style. Includes chapters on domination algorithms and NP-completeness as well as frameworks for domination."
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Yes, you can access Fundamentals of Domination in Graphs by Teresa W. Haynes,Stephen Hedetniemi,Peter Slater in PDF and/or ePUB format, as well as other popular books in Mathematics & Applied Mathematics. We have over one million books available in our catalogue for you to explore.
Information
1.
13
.
MATHEMATICAL
HISTORY
OF
DOMINATION
IN
GRAPHS
39
1.18
(Cockayne,
Fricke,
Hedetniemi
and
Mynhardt
[262))
Define
the
boundary
of
a
set
to
be
the
set
B(S)
=
{v
:
jN[vJ
n
Sl
=
1},
that
is,
the
set
of
vertices
dominated
by
exactly
one
vertex
in
S.
Prove
that
a
dominating
set
Sis
a
minimal
dominating
set
if
and
only
if
B(S)
dominates
S.
1.19
(Wo
lk
[115
0])
Prove
that
if
a
connected
graph
G
do
es
not
contain
either
?4
or
C
4
as
an
induced
subgraph,
then
1(G)
=
1,
that
is,
G
contains
a
vertex
of
degree
n
-
l.
1.20
Prove
Theorem
1.4
that
for
any
graph
G,
1(G)
+
EF(G)
=
n.
EXERCISE
for
Couch
Pot
atoes:
1.21
Determine
!(Kn)·
Table of contents
- Cover
- Half Title
- Title Page
- Copyright Page
- Dedication
- Preface
- Table of Contents
- Prolegomenon
- Chapter 1 Introduction
- Chapter 2 Bounds on the Domination Number
- Chapter 3 Domination, Independence, and Irredundance
- Chapter 4 Efficiency, Redundancy, and Their Duals
- Chapter 5 Changing and Unchanging Domination
- Chapter 6 Conditions on the Dominating Set
- Chapter 7 Varieties of Domination
- Chapter 8 Multiproperty and Multiset Parameters
- Chapter 9 Sums and Products of Parameters
- Chapter 10 Dominating Functions
- Chapter 11 Frameworks for Domination
- Chapter 12 Domination Complexity and Algorithms
- Appendix
- Bibliography
- Notation List
- Index