Sampathkumar, E
(1990)
*The least point covering and domination numbers of a graph.*
Discrete Mathematics, 86 (1-3).
pp. 137-142.

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## Abstract

A set S subset-of V of a graph G = (V, E) is a total point cover (t.p.c.) if S is a point cover containing all isolates of G, if any. The number alpha-t(G) is the minimum cardinality of a t.p.c. A t.p.c. S is a least point cover (l.p.c.) if alpha-t(opening-elbow S closing elbow) less-than-or-equal-to alpha-t(opening elbow S1 closing elbow) for any t.p.c. S1, where opening elbow S closing elbow is the subgraph induced by S. The least point covering number alpha-1(G) of G is the minimum cardinality of a l.p.c. A dominating set D of G is a least dominating set (l.d.s.) if gamma(opening elbow D closing elbow) less-than-or-equal-to gamma(opening elbow D1 closing elbow) for any dominating set D1 (gamma-denotes domination number). The least domination number gamma-1(G) of G is the minimum cardinality of a l.d.s. If gamma-t is the total domination number, we prove among other things: (i) gamma-1 less-than-or-equal-to gamma-t, and (ii) for a tree, gamma-1 less-than-or-equal-to alpha-1.

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

Divisions: | Department of > Mathematics |

Depositing User: | Dr Raju C |

Date Deposited: | 21 Jan 2021 09:54 |

Last Modified: | 27 Jan 2021 06:02 |

URI: | http://eprints.uni-mysore.ac.in/id/eprint/14306 |

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