Abd. Rhani, N. and Mohd. Ali, N. M. and Sarmin, N. H. and Erfanian, A.
(2017)
*On the dominating number, independent number and the regularity of the relative co-prime graph of a group.*
Malaysian Journal of Fundamental and Applied Sciences, 13
(2).
ISSN 2289-5981

Full text not available from this repository.

Official URL: http://dx.doi.org/10.11113/mjfas.v13n2.602

## Abstract

Let H be a subgroup of a finite group G. The co-prime graph of a group is defined as a graph whose vertices are elements of G and two distinct vertices are adjacent if and only if the greatest common divisor of order of x and y is equal to one. This concept has been extended to the relative co-prime graph of a group with respect to a subgroup H, which is defined as a graph whose vertices are elements of G and two distinct vertices x and y are joined by an edge if and only if their orders are co-prime and any of x or y is in H. Some properties of graph such as the dominating number, degree of a dominating set of order one and independent number are obtained. Lastly, the regularity of the relative co-prime graph of a group is found.

Item Type: | Article |
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Uncontrolled Keywords: | co-prime graph, relative co-prime graph, dominating number |

Subjects: | Q Science > QA Mathematics |

Divisions: | Science |

ID Code: | 80920 |

Deposited By: | Narimah Nawil |

Deposited On: | 24 Jul 2019 00:10 |

Last Modified: | 24 Jul 2019 00:10 |

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