# A note on the independent domination number versus the domination number in bipartite graphs

Czechoslovak Mathematical Journal (2017)

- Volume: 67, Issue: 2, page 533-536
- ISSN: 0011-4642

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topWang, Shaohui, and Wei, Bing. "A note on the independent domination number versus the domination number in bipartite graphs." Czechoslovak Mathematical Journal 67.2 (2017): 533-536. <http://eudml.org/doc/288208>.

@article{Wang2017,

abstract = {Let $\gamma (G)$ and $i(G)$ be the domination number and the independent domination number of $G$, respectively. Rad and Volkmann posted a conjecture that $i(G)/ \gamma (G) \le \Delta (G)/2$ for any graph $G$, where $\Delta (G)$ is its maximum degree (see N. J. Rad, L. Volkmann (2013)). In this work, we verify the conjecture for bipartite graphs. Several graph classes attaining the extremal bound and graphs containing odd cycles with the ratio larger than $\Delta (G)/2$ are provided as well.},

author = {Wang, Shaohui, Wei, Bing},

journal = {Czechoslovak Mathematical Journal},

keywords = {domination; independent domination},

language = {eng},

number = {2},

pages = {533-536},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {A note on the independent domination number versus the domination number in bipartite graphs},

url = {http://eudml.org/doc/288208},

volume = {67},

year = {2017},

}

TY - JOUR

AU - Wang, Shaohui

AU - Wei, Bing

TI - A note on the independent domination number versus the domination number in bipartite graphs

JO - Czechoslovak Mathematical Journal

PY - 2017

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 67

IS - 2

SP - 533

EP - 536

AB - Let $\gamma (G)$ and $i(G)$ be the domination number and the independent domination number of $G$, respectively. Rad and Volkmann posted a conjecture that $i(G)/ \gamma (G) \le \Delta (G)/2$ for any graph $G$, where $\Delta (G)$ is its maximum degree (see N. J. Rad, L. Volkmann (2013)). In this work, we verify the conjecture for bipartite graphs. Several graph classes attaining the extremal bound and graphs containing odd cycles with the ratio larger than $\Delta (G)/2$ are provided as well.

LA - eng

KW - domination; independent domination

UR - http://eudml.org/doc/288208

ER -

## References

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