# Domination number of graph fractional powers

Document Type : Research Paper

Author

Shahid Beheshti University

Abstract

For any $k \in \mathbb{N}$, the $k$-subdivision of graph $G$ is a simple graph $G^{\frac{1}{k}}$, which is constructed by replacing each edge of $G$ with a path of length $k$. In [Moharram N. Iradmusa, On colorings of graph fractional powers, Discrete Math., (310) 2010, No. 10-11, 1551-1556] the $m$th power of the $n$-subdivision of $G$ has been introduced as a fractional power of $G$, denoted by $G^{\frac{m}{n}}$. In this regard, we investigate domination number and independent domination number of fractional powers of graphs.

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### History

• Receive Date: 01 January 2013
• Revise Date: 29 October 2013
• Accept Date: 01 November 2013
• First Publish Date: 01 December 2014