Abstract:
For a connected graph GG of order at least two, a double monophonic set SS of a graph GG is a restrained double monophonic set if either S=VS=V or the subgraph induced by V−SV−S has no isolated vertices. The minimum cardinality of a restrained double monophonic set of GG is the restrained double monophonic number of GG and is denoted by dmr(G)dmr(G). The restrained double monophonic number of certain classes graphs are determined. It is shown that for any integers a,b,ca,b,c with 3≤a≤b≤c3≤a≤b≤c, there is a connected graph GG with m(G)=am(G)=a, mr(G)=bmr(G)=b and dmr(G)=cdmr(G)=c, where m(G)m(G) is the monophonic number and mr(G)mr(G) is the restrained monophonic number of a graph GG.
\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