The upper connected outer connected monophonic number of a graph. Issue 1 (2nd January 2023)

• Record Type: Journal Article
• Authors: Ganesamoorthy, K.; Lakshmi Priya, S.
• Is Part Of: International journal of computer mathematics. Volume 8:Issue 1(2023)
• Page Start: 57
• Page End: 66
• Publication Date: 2023-01-02
• Subjects: Monophonic set -- outer connected monophonic set -- connected outer connected monophonic set -- minimal connected outer connected monophonic set -- upper connected outer connected monophonic number; 05C12; Computer systems -- Periodicals; Computer systems; Periodicals; 004
• DOI: 10.1080/23799927.2023.2184722
• Languages: English
• ISSNs: 2379-9927

Abstract

Abstract : For a connected graph G of order at least two, a connected outer connected 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 c m c o + ( 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 certain 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 c m c o ( G ) = a and c m c o + ( G ) = b . Also, for any three integers a, b and n with 4 ≤ a ≤ n ≤ b, there is a connected graph G with c m c o ( G ) = a and c m c o + ( G ) = b and a minimal connected outer connected monophonic set of cardinality n, where c m c o ( G ) is the connected outer connected monophonic number of a graph.