Abstract:
For a connected graph G of order at least two, a double monophonic set S of a graph G is a restrained double monophonic set if either S=V or the subgraph induced by V−S has no isolated vertices. The minimum cardinality of a restrained double monophonic set of G is the restrained double monophonic number of G and is denoted by dmr(G). The restrained double monophonic number of certain classes graphs are determined. It is shown that for any integers a,b,c with 3≤a≤b≤c, there is a connected graph G with m(G)=a, mr(G)=b and dmr(G)=c, where m(G) is the monophonic number and mr(G) is the restrained monophonic number of a graph G.
\Bibitem{SanGan19}
\by A.~P.~Santhakumaran, K.~Ganesamoorthy
\paper Restrained double monophonic number of a graph
\jour Ural Math. J.
\yr 2019
\vol 5
\issue 2
\pages 55--63
\mathnet{http://mi.mathnet.ru/umj102}
\crossref{https://doi.org/10.15826/umj.2019.2.005}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=MR4054650}
\zmath{https://zbmath.org/?q=an:1448.05122}
\elib{https://elibrary.ru/item.asp?id=41672793}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85078778582}
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https://www.mathnet.ru/eng/umj102
https://www.mathnet.ru/eng/umj/v5/i2/p55
This publication is cited in the following 1 articles:
K. Ganesamoorthy, S. Lakshmi Priya, “The upper connected outer connected monophonic number of a graph”, International Journal of Computer Mathematics: Computer Systems Theory, 8:1 (2023), 57