### Abstract

Two vertices u,w ϵ V, vv-dominate each other if they are incident on the same block. A set S ⊆ V is a vv-dominating set (VVD-set) if every vertex in V-S is vv-dominated by a vertex in S. The vv-domination number = γ_{vv}(G) is the cardinality of a minimum VVD-set of G. Two blocks b1, b2 ϵ B(G) the set of all blocks of G, bb-dominate each other if there is a common cutpoint. A set L ⊆ B(G) is said to be a bb-dominating set (BBD set) if every block in B(G)-L is bb-dominated by some block in L. The bb-domination number γ_{bb} = γ_{bb}(G) is the cardinality of a minimum BBD-set of G. A vertex v and a block b are said to b-dominate each other if v is incident on the block b. Then vb-domination number γ_{vb} = γ_{vb}(G) (bv-domination number γ_{bv} = γ_{bv}(G)) is the minimum number of vertices (blocks) needed to b-dominate all the blocks (vertices) of G. In this paper we study the properties of these block domination parameters and establish a relation between these parameters giving an inequality chain consisting of nine parameters.

Original language | English |
---|---|

Article number | 1350018 |

Journal | Discrete Mathematics, Algorithms and Applications |

Volume | 5 |

Issue number | 3 |

DOIs | |

Publication status | Published - 01-09-2013 |

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### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics

### Cite this

*Discrete Mathematics, Algorithms and Applications*,

*5*(3), [1350018]. https://doi.org/10.1142/S1793830913500183

}

*Discrete Mathematics, Algorithms and Applications*, vol. 5, no. 3, 1350018. https://doi.org/10.1142/S1793830913500183

**RELATIONSHIP between BLOCK DOMINATION PARAMETERS of A GRAPH.** / Bhat, P. G.; Bhat, R. S.; Bhat, Surekha R.

Research output: Contribution to journal › Article

TY - JOUR

T1 - RELATIONSHIP between BLOCK DOMINATION PARAMETERS of A GRAPH

AU - Bhat, P. G.

AU - Bhat, R. S.

AU - Bhat, Surekha R.

PY - 2013/9/1

Y1 - 2013/9/1

N2 - Two vertices u,w ϵ V, vv-dominate each other if they are incident on the same block. A set S ⊆ V is a vv-dominating set (VVD-set) if every vertex in V-S is vv-dominated by a vertex in S. The vv-domination number = γvv(G) is the cardinality of a minimum VVD-set of G. Two blocks b1, b2 ϵ B(G) the set of all blocks of G, bb-dominate each other if there is a common cutpoint. A set L ⊆ B(G) is said to be a bb-dominating set (BBD set) if every block in B(G)-L is bb-dominated by some block in L. The bb-domination number γbb = γbb(G) is the cardinality of a minimum BBD-set of G. A vertex v and a block b are said to b-dominate each other if v is incident on the block b. Then vb-domination number γvb = γvb(G) (bv-domination number γbv = γbv(G)) is the minimum number of vertices (blocks) needed to b-dominate all the blocks (vertices) of G. In this paper we study the properties of these block domination parameters and establish a relation between these parameters giving an inequality chain consisting of nine parameters.

AB - Two vertices u,w ϵ V, vv-dominate each other if they are incident on the same block. A set S ⊆ V is a vv-dominating set (VVD-set) if every vertex in V-S is vv-dominated by a vertex in S. The vv-domination number = γvv(G) is the cardinality of a minimum VVD-set of G. Two blocks b1, b2 ϵ B(G) the set of all blocks of G, bb-dominate each other if there is a common cutpoint. A set L ⊆ B(G) is said to be a bb-dominating set (BBD set) if every block in B(G)-L is bb-dominated by some block in L. The bb-domination number γbb = γbb(G) is the cardinality of a minimum BBD-set of G. A vertex v and a block b are said to b-dominate each other if v is incident on the block b. Then vb-domination number γvb = γvb(G) (bv-domination number γbv = γbv(G)) is the minimum number of vertices (blocks) needed to b-dominate all the blocks (vertices) of G. In this paper we study the properties of these block domination parameters and establish a relation between these parameters giving an inequality chain consisting of nine parameters.

UR - http://www.scopus.com/inward/record.url?scp=85011599478&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85011599478&partnerID=8YFLogxK

U2 - 10.1142/S1793830913500183

DO - 10.1142/S1793830913500183

M3 - Article

AN - SCOPUS:85011599478

VL - 5

JO - Discrete Mathematics, Algorithms and Applications

JF - Discrete Mathematics, Algorithms and Applications

SN - 1793-8309

IS - 3

M1 - 1350018

ER -