Minimal total open monophonic sets in graphs. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Santhakumaran, A. P.; Mahendran, M.; Simon Raj, F.; Ganesamoorthy, K.
• Is Part Of: International journal of computer mathematics. Volume 7:Issue 1(2022)
• Page Start: 6
• Page End: 15
• Publication Date: 2022-01-02
• Subjects: Total open monophonic set -- total open monophonic number -- minimal total open monophonic set -- upper total open monophonic number; 05C12; Computer systems -- Periodicals; Computer systems; Periodicals; 004
• DOI: 10.1080/23799927.2021.1974568
• Languages: English
• ISSNs: 2379-9927

Abstract

Abstract : For a connected graph G of order n, a total open monophonic set S of vertices in a graph G is a minimal total open monophonic set if no proper subset of S is a total open monophonic set of G . The upper total open monophonic number o m t + ( G ) of G is the maximum cardinality of a minimal total open monophonic set of G . Certain general properties regarding minimal total open monophonic sets are discussed, and also the upper total open monophonic numbers of certain standard graphs are determined. It is proved that o m t + ( G ) = 4 for the Petersen graph G . For integers n and a with 2 ≤ a ≤ n, n ≥ a + 3, it is shown that there exists a connected graph G of order n with o m ( G ) = a, o m t ( G ) = a + 1 and o m t + ( G ) = a + 2 .