Affiliations: [a] Department of Science and Humanities, University College of Engineering Nagercoil, Anna University, Tirunelveli Region, Nagercoil, India
| [b] Department of Mathematics, Scott Christian College (Autonomous), Nagercoil, India
| [c] Department of Computer Science and Engineering, Sejong University, Seoul, Korea
| [d] Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi, India
Correspondence:
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Corresponding author. J. Ajitha Fancy, Department of Mathematics, Scott Christian College (Autonomous), Nagercoil - 629 003, India. E-mail: [email protected].
Abstract: A set S ⊆ V in a graph G is a MED-set if every vertex in V - S has a monophonic eccentric vertex in S. The MED-number γme (G) is the cardinality of a minimum MED-set of G. A set S ⊆ V in a graph G is a CMED-set if S is a MED-set and the induced subgraph is connected. The CMED-number γcme (G) is the cardinality of a minimum CMED-set of G. We investigate some properties of the CMED-sets. Also, we determine the bounds of the CMED-number and find the same for some standard graphs. The CMED-number has applications in security based communication networks in real life situations. This motivated us to introduce and investigate CMED-set in a graph.