The connected monophonic eccentric domination number of a graph

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.