Naji, A. M. and Soner, N. D.
(2015)
*Resolving connected domination in graphs.*
International Journal of Mathematical Combinatorics, 4.
pp. 129-136.

## Abstract

For an ordered subset W = w1,w2, Â· Â· Â· ,wk of vertices and a vertex v in a connected graph G = (V,E), the (metric) representation of v with respect to W is the k-vector r(v|W) = (d(v,w1), d(v,w2), Â· Â· Â· , d(v,wk)). The set W is a resolving set for G if distinct vertices of G have distinct representations with respect to W. A resolving set of minimum cardinality is called a minimum resolving set and the cardinality of it is a dimension of G, denoted by dim(G). In this paper, we introduce resolving connected domination number rc(G) of graphs. We investigate the relationship between resolving connected domination number, connected domination number, resolving domination number and dimension of a graph G. Bounds for rc(G) are determined. Exact values of rc(G) for some standard graphs are found

Item Type: | Article |
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Uncontrolled Keywords: | Resolving Dominating Set and Resolving Connected Dominating Set and Resolving Connected Domination Number and Dimension of a Graph |

Subjects: | E Mathematical Science > Mathematics |

Divisions: | Department of > Mathematics |

Depositing User: | Shrirekha N |

Date Deposited: | 20 Jun 2019 06:20 |

Last Modified: | 10 Dec 2019 09:34 |

URI: | http://eprints.uni-mysore.ac.in/id/eprint/3473 |

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