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Reseach Article
Connected Edge Monophonic Domination Number of a Graph
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 145 - Number 12 |
| Year of Publication: 2016 |
| Authors: P. Arul Paul Sudhahar, M. Mohammed Abdul Khayyoom, A. Sadiquali |
10.5120/ijca2016910759
|
P. Arul Paul Sudhahar, M. Mohammed Abdul Khayyoom, A. Sadiquali . Connected Edge Monophonic Domination Number of a Graph. International Journal of Computer Applications. 145, 12 ( Jul 2016), 18-21. DOI=10.5120/ijca2016910759
Abstract
In this paper the concept of connected edge monophonic domination number of a graph is introduced. A set of vertices M of a graph G is a connected edge monophonic domination set (CEMD set) if it is edge monophonic set, a domination set of G and the induced sub graph is connected. The connected edge monophonic domination number (CEMD number) of G, γmce (G) is the cardinality of a minimum CEMD set. CEMD number of some connected graphs are realized. Connected graphs of order n with CEMD number n are characterised.It is shown that for every pair of integers m and n such that 3 ≤ m ≤ n, there exist a connected graph G of order n with γmce (G) = m. Also, for any positive integers p,q and r there is a connected graph G such that m(G)= p,me(G)= q and γmce (G) =r. Again, for any connected graph G, γmce (G) lies between n/(1+∆(G)) and n.
References
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