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.
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U2 - 10.1142/S1793830913500183
DO - 10.1142/S1793830913500183
M3 - Article
AN - SCOPUS:85011599478
SN - 1793-8309
VL - 5
JO - Discrete Mathematics, Algorithms and Applications
JF - Discrete Mathematics, Algorithms and Applications
IS - 3
M1 - 1350018
ER -