On the connected monophonic number of a graph. Issue 2 (3rd April 2022)

• Record Type: Journal Article
• Authors: Ganesamoorthy, K.; Murugan, M.; Santhakumaran, A. P.
• Is Part Of: International journal of computer mathematics. Volume 7:Issue 2(2022)
• Page Start: 139
• Page End: 148
• Publication Date: 2022-04-03
• Subjects: Connected monophonic set -- connected monophonic number -- extreme-cut order -- extreme-cut connected monophonic graph; 05C12; Computer systems -- Periodicals; Computer systems; Periodicals; 004
• DOI: 10.1080/23799927.2022.2071765
• Languages: English
• ISSNs: 2379-9927

Abstract

Abstract : 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 m c ( G ) . The number of extreme vertices and cut-vertices of G is its extreme-cut order e c ( G ) . A graph G is an extreme-cut connected monophonic graph if m c ( G ) = e c ( G ) . Some interesting results on the extreme-cut connected monophonic graphs G are studied. For positive integers r, d and k ≥ 5 with r < d, there exists an extreme-cut connected monophonic graph G with monophonic radius r, monophonic diameter d and the connected monophonic number k . Also if p, d and k are positive integers such that 2 ≤ d ≤ k − 3 and p − d + k ≥ 0, then there exists an extreme-cut connected monophonic graph G of order p with monophonic diameter d and m c ( G ) = k .