Total Version of the Domination Game

Michael A. Henning; Sandi Klavžar; Douglas F. Rall

doi:10.1007/s00373-014-1470-9

Total Version of the Domination Game

Michael A. Henning, Sandi Klavžar, Douglas F. Rall

Mathematics and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

61 Citations (Scopus)

Abstract

In this paper, we continue the study of the domination game in graphs introduced by Brešar et al. (SIAM J Discret Math 24:979–991, 2010). We study the total version of the domination game and show that these two versions differ significantly. We present a key lemma, known as the Total Continuation Principle, to compare the Dominator-start total domination game and the Staller-start total domination game. Relationships between the game total domination number and the total domination number, as well as between the game total domination number and the domination number, are established.

Original language	English
Pages (from-to)	1453-1462
Number of pages	10
Journal	Graphs and Combinatorics
Volume	31
Issue number	5
DOIs	https://doi.org/10.1007/s00373-014-1470-9
Publication status	Published - 24 Sept 2015

Keywords

Domination game
Total domination number

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

Access to Document

10.1007/s00373-014-1470-9

Cite this

@article{5caf1444db284a0584f9ed9c07239723,

title = "Total Version of the Domination Game",

abstract = "In this paper, we continue the study of the domination game in graphs introduced by Bre{\v s}ar et al. (SIAM J Discret Math 24:979–991, 2010). We study the total version of the domination game and show that these two versions differ significantly. We present a key lemma, known as the Total Continuation Principle, to compare the Dominator-start total domination game and the Staller-start total domination game. Relationships between the game total domination number and the total domination number, as well as between the game total domination number and the domination number, are established.",

keywords = "Domination game, Total domination number",

author = "Henning, {Michael A.} and Sandi Klav{\v z}ar and Rall, {Douglas F.}",

note = "Publisher Copyright: {\textcopyright} 2014, Springer Japan.",

year = "2015",

month = sep,

day = "24",

doi = "10.1007/s00373-014-1470-9",

language = "English",

volume = "31",

pages = "1453--1462",

journal = "Graphs and Combinatorics",

issn = "0911-0119",

publisher = "Springer Japan",

number = "5",

}

TY - JOUR

T1 - Total Version of the Domination Game

AU - Henning, Michael A.

AU - Klavžar, Sandi

AU - Rall, Douglas F.

PY - 2015/9/24

Y1 - 2015/9/24

N2 - In this paper, we continue the study of the domination game in graphs introduced by Brešar et al. (SIAM J Discret Math 24:979–991, 2010). We study the total version of the domination game and show that these two versions differ significantly. We present a key lemma, known as the Total Continuation Principle, to compare the Dominator-start total domination game and the Staller-start total domination game. Relationships between the game total domination number and the total domination number, as well as between the game total domination number and the domination number, are established.

AB - In this paper, we continue the study of the domination game in graphs introduced by Brešar et al. (SIAM J Discret Math 24:979–991, 2010). We study the total version of the domination game and show that these two versions differ significantly. We present a key lemma, known as the Total Continuation Principle, to compare the Dominator-start total domination game and the Staller-start total domination game. Relationships between the game total domination number and the total domination number, as well as between the game total domination number and the domination number, are established.

KW - Domination game

KW - Total domination number

UR - http://www.scopus.com/inward/record.url?scp=84940438890&partnerID=8YFLogxK

U2 - 10.1007/s00373-014-1470-9

DO - 10.1007/s00373-014-1470-9

M3 - Article

AN - SCOPUS:84940438890

SN - 0911-0119

VL - 31

SP - 1453

EP - 1462

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

IS - 5

ER -

Total Version of the Domination Game

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this