# RELATIONSHIP between BLOCK DOMINATION PARAMETERS of A GRAPH

P. G. Bhat, R. S. Bhat, Surekha R. Bhat

Research output: Contribution to journalArticle

4 Citations (Scopus)

### 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 = 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.

Original language English 1350018 Discrete Mathematics, Algorithms and Applications 5 3 https://doi.org/10.1142/S1793830913500183 Published - 01-09-2013

### Fingerprint

Domination number
Dominating Set
Cardinality
Vertex of a graph
Domination

### All Science Journal Classification (ASJC) codes

• Discrete Mathematics and Combinatorics

### Cite this

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

In: Discrete Mathematics, Algorithms and Applications, Vol. 5, No. 3, 1350018, 01.09.2013.

Research output: Contribution to journalArticle

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