Abstract Paper
| Title | : Bounds on the Connected Domination in Graphs |
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| Author(s) | : 1 J.Vinolin , 2 D.S.T.Ramesh, 3 S.Athisayanathan and 4 A.Anto Kinsley |
| Article Information | : , 1-14 |
| Affiliation(s) | : 1,3,4 Department of Mathematics, St. Xaviers College, Palayamkottai, Manonmaniam Sundaranar University, Tirunelveli - 627012, Tamil Nadu, India. |
| : 2 Department of Mathematics, Margchosis College, Nazareth, Manonmaniam Sundaranar University, Tirunelveli - 627012, Tamil Nadu, India. |
Abstract :
A set Sā V of a connected graph G is a hop dominating set of G if for every vertex v in V ā S there exists a vertex u in S such that d(u, v) = 2. The cardinality of a minimum hop dominating set of G is called the hop domination number and is denoted by Ī³h (G). A hop dominating set D of a graph G is said to be a connected hop dominating set of G if the induced subgraph <D> is connected. The cardinality of a minimum connected hop dominating set is called the connected hop dominationnumber of G and it is denoted by š¾_ā^c(G). In this paper some graphs G are characterized for which Ī³_h(G) = 2. Bounds based on diameter, girth and maximum degree for Ī³_h(G) are developed. In addition the hop domination number of wounded spider is computed. The hop dominating sets are compared to the distance ā2 dominating sets. An important result is proved that if G_1, G_2, ā¦,G_s are the connected proper subgraphs of G with minimum connected hop dominating sets D_1, D_2, ā¦, D_s as then š¾_ā^c(G)ā¤ Ī£_{i=1}^{s} š¾_ā^c(G_i) + 2s.
| Keywords | : Graphs, distance, domination number, distance domination number, Hop domination number, Connected Hop domination number |
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| Document Type | : Research Paper |
| DOI | : Bounds on the Connected Domination in Graphs |
| Publication date | : July 09, 2018 |