"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 & Mathematics General. We have over one million books available in our catalogue for you to explore.

Information

Publisher

CRC Press

Year

2013

ISBN

9781482246582

Edition

Topic

Mathematics

Subtopic

Mathematics General

Index

Mathematics

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)· 

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