Alwardi, A. and Soner, N. D.
(2013)
*The P3-domination in graphs.*
Advanced Studies in Contemporary Mathematics (Kyungshang), 23 (1).
pp. 183-194.

## Abstract

Let G be a graph and u,v be any vertices of G. Then u and v are said to be P3-adjacent vertices of G if there is a subgraph of G, isomorphic to P3, Containing u and v. A P3-dominating set of G is a set D of vertices such that every vertex of G belongs to D or is P 3-adjacent to a vertex of D. The P3-domination number of G denoted by Î³P3(G) is the minimum cardinality among the P 3-dominating sets of vertices of G. In this paper we introduce and study the P3-domination of a graph G and analogous to this concept we define the P3-independence number Î²P3(G), P 3-neighbourhood number Î·P3(G) and P 3-domatic number dp3(G). Some bounds and interesting results are obtained. Also the P3-adjacency motivated us to define new graphs in particular P3-neighbourhood graph, P 3-complete graph, P3regular graph, P3- complement graph and P3-complementary graph, some basic properties of these graphs are introduce and new method to construct any r-regular graph is established, finally we generalize the domination of graphs.

Item Type: | Article |
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Subjects: | E Mathematical Science > Mathematics |

Divisions: | Department of > Mathematics |

Depositing User: | Arshiya Kousar Library Assistant |

Date Deposited: | 09 Sep 2019 09:50 |

Last Modified: | 09 Sep 2019 09:50 |

URI: | http://eprints.uni-mysore.ac.in/id/eprint/7848 |

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