The upper connected outer connected monophonic number of a graph

For a connected graph of order at least two, a connected outer connected monophonic set of is called a minimal connected outer connected monophonic set if no proper subset of is a connected outer connected monophonic set of . The upper connected outer connected monophonic number of is the maximum ca...

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Bibliographic Details
Published in:International journal of computer mathematics. Computer systems theory 2023-01, Vol.8 (1), p.57-66
Main Authors: Ganesamoorthy, K., Lakshmi Priya, S.
Format: Article
Language:English
Subjects:
connected outer connected monophonic set
minimal connected outer connected monophonic set
Monophonic set
outer connected monophonic set
upper connected outer connected monophonic number
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Summary:For a connected graph of order at least two, a connected outer connected monophonic set of is called a minimal connected outer connected monophonic set if no proper subset of is a connected outer connected monophonic set of . The upper connected outer connected monophonic number of is the maximum cardinality of a minimal connected outer connected monophonic set of . 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 with , there is a connected graph of order with and . Also, for any three integers and with , there is a connected graph with and and a minimal connected outer connected monophonic set of cardinality , where is the connected outer connected monophonic number of a graph.
ISSN:2379-9927
2379-9935
DOI:10.1080/23799927.2023.2184722