The upper connected outer connected monophonic number of a graph

For a connected graph G of order at least two, a connected outer con-nected monophonic set S of G is called a minimal connected outer connected monophonic set if no proper subset of S is a connected outer connected monophonic set of G. The upper connected outer connected monophonic number cm(co)(+)(G) of G is the maximum cardinality of a minimal connected outer connected monophonic set of G. We determine bounds for it and find the upper connected outer connected monophonic number of cer-tain classes of graphs. It is shown that for any two integers a, b with 4 < a < b < p - 2, there is a connected graph G of order p with cmco(G) = a and cm(co)(+)(G) = b. Also, for any three integers a, b and n with 4 < a < n < b, there isa connected graph G with cm(co)(G) = a and cm(co)(+)(G) = b and a min-imal connected outer connected monophonic set of cardinality n, where cmco(G) is the connected outer connected monophonic number of a graph.