A note on the domination dot-critical graphs

Xue gang Chen; Wai Chee Shiu

doi:10.1016/j.dam.2009.07.014

A note on the domination dot-critical graphs

Xue gang Chen^*, Wai Chee Shiu

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

4 Citations (Scopus)

Abstract

A graph G is dot-critical if contracting any edge decreases the domination number. Nader Jafari Rad (2009) [3] posed the problem: Is it true that a connected k-dot-critical graph G with G^′ = 0{combining long solidus overlay} is 2-connected? In this note, we give a family of 1-connected 2 k-dot-critical graph with G^′ = 0{combining long solidus overlay} and show that this problem has a negative answer.

Original language	English
Pages (from-to)	3743-3745
Number of pages	3
Journal	Discrete Applied Mathematics
Volume	157
Issue number	18
DOIs	https://doi.org/10.1016/j.dam.2009.07.014
Publication status	Published - 28 Nov 2009

Scopus Subject Areas

Discrete Mathematics and Combinatorics
Applied Mathematics

User-Defined Keywords

Complete bipartite graph
Domination dot-critical
Domination number

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10.1016/j.dam.2009.07.014

Cite this

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title = "A note on the domination dot-critical graphs",

abstract = "A graph G is dot-critical if contracting any edge decreases the domination number. Nader Jafari Rad (2009) [3] posed the problem: Is it true that a connected k-dot-critical graph G with G′ = 0{combining long solidus overlay} is 2-connected? In this note, we give a family of 1-connected 2 k-dot-critical graph with G′ = 0{combining long solidus overlay} and show that this problem has a negative answer.",

keywords = "Complete bipartite graph, Domination dot-critical, Domination number",

author = "Chen, {Xue gang} and Shiu, {Wai Chee}",

note = "Funding Information: This work is supported by GRF, Research Grant Council of Hong Kong; FRG, Hong Kong Baptist University. ",

year = "2009",

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doi = "10.1016/j.dam.2009.07.014",

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T1 - A note on the domination dot-critical graphs

AU - Chen, Xue gang

AU - Shiu, Wai Chee

N1 - Funding Information: This work is supported by GRF, Research Grant Council of Hong Kong; FRG, Hong Kong Baptist University.

PY - 2009/11/28

Y1 - 2009/11/28

N2 - A graph G is dot-critical if contracting any edge decreases the domination number. Nader Jafari Rad (2009) [3] posed the problem: Is it true that a connected k-dot-critical graph G with G′ = 0{combining long solidus overlay} is 2-connected? In this note, we give a family of 1-connected 2 k-dot-critical graph with G′ = 0{combining long solidus overlay} and show that this problem has a negative answer.

AB - A graph G is dot-critical if contracting any edge decreases the domination number. Nader Jafari Rad (2009) [3] posed the problem: Is it true that a connected k-dot-critical graph G with G′ = 0{combining long solidus overlay} is 2-connected? In this note, we give a family of 1-connected 2 k-dot-critical graph with G′ = 0{combining long solidus overlay} and show that this problem has a negative answer.

KW - Complete bipartite graph

KW - Domination dot-critical

KW - Domination number

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DO - 10.1016/j.dam.2009.07.014

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EP - 3745

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

IS - 18

ER -

A note on the domination dot-critical graphs

Abstract

Scopus Subject Areas

User-Defined Keywords

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