The Upper Complement Connected Monophonic Number of a Graph
F. Merlin Sugirtha1, P.Arul Paul Sudhakar2, S.Robinson Chellathurai3
1F. Merlin Sugirtha, Register Number-12447,Scott Christian College, Nagercoil-629 003, India.
2P. Arul Paul Sudhakar, Assistant Professor, Department of Mathematics,Rani Anna Government Arts College (W), Tirunelveli-627 012, India.
3S.Robinson Chellathurai, Associate Professor, Department of Mathematics, Scott Christian College, Nagercoil-629 003, India
Manuscript received on 02 October 2019 | Revised Manuscript received on 13 October 2019 | Manuscript Published on 29 June 2020 | PP: 297-300 | Volume-8 Issue-10S2 August 2019 | Retrieval Number: J105308810S19/2019©BEIESP | DOI: 10.35940/ijitee.J1053.08810S19
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: For a connected graph G=(V, E), a monophonic set M of G of is said to be a complement connected monophonic set if M=V or the subgraph 〈V-M〉 is connected. The minimum cardinality of a complement connected monophonic set of G is the complement connected monophonic number if G and is denoted by mcc(G).A complement connected monophonic set M in a connected graph G is called a minimal complement connected monophonic set of no proper subset of M is a complement connected monophonic set of M The upper complement connected monophonic number m+cc (G) of G is the maximum cardinality of a minimal complement connected monophonic set ofG. Some general properties under this concept are studied. The upper complement connected monophonic number of some standard graphs are determined. Some of its general properties are studied. It is shown that for any positive integers 2 ≤ a ≤b, there exists a connected graph G such that mcc(G) = a and m+cc(G) =b.
Keywords: Monophonic Path, Complement Connected Monophonic Number, Upper Complement Connected Monophonic Number.
Scope of the Article: Applied Mathematics and Mechanics