On the connected monophonic number of a graph
Kathiresan Ganesamoorthy, Muniyappan Murugan, A. P. Santhakumaran · International Journal of Computer Mathematics Computer Systems Theory · 2022
For a connected graph G of order at least two, a connected monophonic set of G is a monophonic set S such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected monophonic set of G is the connected monophonic number of G and is denoted by mc(G). The number of extreme vertices and cut-vertices of G is its extreme-cut order ec(G). A graph G is an extreme-cut connected monophonic graph if mc(G)=ec(G). Some interesting results on the extreme-cut connected monophonic graphs G are studied. For positive integers r, d and k≥5 with r