Abstract
Let G = (V, X) be a semigraph. A set D ⊆ V is called adjacent dominating set (ad-set) if for every υ ∈ V - D there exists a u ∈ D such that u is adjacent to v. The adjacency domination number γa = γa(G) is the minimum cardinality of an ad-set of G. Let Ve be the set of all end vertices in G. A set D ⊆ Ve is called end vertex adjacent dominating set (ead-set) if (i) D is an ad-set and (ii) Every end vertex υ ∈ V - D is e-adjacent to some end vertex u ∈ D in G. The end vertex adjacency domination number γea = γea(G) is the minimum cardinality of an ead-set of G. A set D C V is called consecutive adjacent dominating set (cad-set) if for every υ ∈ V - D there exists a u ∈ D such that u is ca-adjacent to v in G. The consecutive adjacency domination number γca = γca(G) is the minimum cardinality of a cad set of G. The above domination parameters are determined for various semigraphs and a few bounds are obtained.
| Original language | English |
|---|---|
| Pages (from-to) | 106-111 |
| Number of pages | 6 |
| Journal | Electronic Notes in Discrete Mathematics |
| Volume | 15 |
| DOIs | |
| Publication status | Published - 01-05-2003 |
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All Science Journal Classification (ASJC) codes
- Applied Mathematics
- Discrete Mathematics and Combinatorics
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Domination in Semigraphs. / Kamath, S. S.; Bhat, R. S.
In: Electronic Notes in Discrete Mathematics, Vol. 15, 01.05.2003, p. 106-111.Research output: Contribution to journal › Article
TY - JOUR
T1 - Domination in Semigraphs
AU - Kamath, S. S.
AU - Bhat, R. S.
PY - 2003/5/1
Y1 - 2003/5/1
N2 - Let G = (V, X) be a semigraph. A set D ⊆ V is called adjacent dominating set (ad-set) if for every υ ∈ V - D there exists a u ∈ D such that u is adjacent to v. The adjacency domination number γa = γa(G) is the minimum cardinality of an ad-set of G. Let Ve be the set of all end vertices in G. A set D ⊆ Ve is called end vertex adjacent dominating set (ead-set) if (i) D is an ad-set and (ii) Every end vertex υ ∈ V - D is e-adjacent to some end vertex u ∈ D in G. The end vertex adjacency domination number γea = γea(G) is the minimum cardinality of an ead-set of G. A set D C V is called consecutive adjacent dominating set (cad-set) if for every υ ∈ V - D there exists a u ∈ D such that u is ca-adjacent to v in G. The consecutive adjacency domination number γca = γca(G) is the minimum cardinality of a cad set of G. The above domination parameters are determined for various semigraphs and a few bounds are obtained.
AB - Let G = (V, X) be a semigraph. A set D ⊆ V is called adjacent dominating set (ad-set) if for every υ ∈ V - D there exists a u ∈ D such that u is adjacent to v. The adjacency domination number γa = γa(G) is the minimum cardinality of an ad-set of G. Let Ve be the set of all end vertices in G. A set D ⊆ Ve is called end vertex adjacent dominating set (ead-set) if (i) D is an ad-set and (ii) Every end vertex υ ∈ V - D is e-adjacent to some end vertex u ∈ D in G. The end vertex adjacency domination number γea = γea(G) is the minimum cardinality of an ead-set of G. A set D C V is called consecutive adjacent dominating set (cad-set) if for every υ ∈ V - D there exists a u ∈ D such that u is ca-adjacent to v in G. The consecutive adjacency domination number γca = γca(G) is the minimum cardinality of a cad set of G. The above domination parameters are determined for various semigraphs and a few bounds are obtained.
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UR - http://www.scopus.com/inward/citedby.url?scp=34247141431&partnerID=8YFLogxK
U2 - 10.1016/S1571-0653(04)00548-7
DO - 10.1016/S1571-0653(04)00548-7
M3 - Article
AN - SCOPUS:34247141431
VL - 15
SP - 106
EP - 111
JO - Electronic Notes in Discrete Mathematics
JF - Electronic Notes in Discrete Mathematics
SN - 1571-0653
ER -