# Perfect connected-dominant graphs

Discussiones Mathematicae Graph Theory (2003)

- Volume: 23, Issue: 1, page 159-162
- ISSN: 2083-5892

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topIgor Edmundovich Zverovich. "Perfect connected-dominant graphs." Discussiones Mathematicae Graph Theory 23.1 (2003): 159-162. <http://eudml.org/doc/270408>.

@article{IgorEdmundovichZverovich2003,

abstract = {If D is a dominating set and the induced subgraph G(D) is connected, then D is a connected dominating set. The minimum size of a connected dominating set in G is called connected domination number $γ_c(G)$ of G. A graph G is called a perfect connected-dominant graph if $γ(H) = γ_c(H)$ for each connected induced subgraph H of G.We prove that a graph is a perfect connected-dominant graph if and only if it contains no induced path P₅ and induced cycle C₅.},

author = {Igor Edmundovich Zverovich},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {Connected domination; perfect connected-dominant graph; connected domination; domination number},

language = {eng},

number = {1},

pages = {159-162},

title = {Perfect connected-dominant graphs},

url = {http://eudml.org/doc/270408},

volume = {23},

year = {2003},

}

TY - JOUR

AU - Igor Edmundovich Zverovich

TI - Perfect connected-dominant graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2003

VL - 23

IS - 1

SP - 159

EP - 162

AB - If D is a dominating set and the induced subgraph G(D) is connected, then D is a connected dominating set. The minimum size of a connected dominating set in G is called connected domination number $γ_c(G)$ of G. A graph G is called a perfect connected-dominant graph if $γ(H) = γ_c(H)$ for each connected induced subgraph H of G.We prove that a graph is a perfect connected-dominant graph if and only if it contains no induced path P₅ and induced cycle C₅.

LA - eng

KW - Connected domination; perfect connected-dominant graph; connected domination; domination number

UR - http://eudml.org/doc/270408

ER -

## References

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