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Ural Mathematical Journal, 2019, Volume 5, Issue 2, Pages 55–63
DOI: https://doi.org/10.15826/umj.2019.2.005
(Mi umj102)
 

This article is cited in 1 scientific paper (total in 1 paper)

Restrained double monophonic number of a graph

A. P. Santhakumarana, K. Ganesamoorthyb

a Department of Mathematics, Hindustan Institute of Technology and Science, Chennai – 603 103, India
b Department of Mathematics, Coimbatore Institute of Technology, Coimbatore – 641 014, India
Full-text PDF (141 kB) Citations (1)
References:
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 VSVS 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 3abc3abc, 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.
Keywords: Monophonic set, Restrained monophonic set, Restrained monophonic number, Restrained double monophonic set, Restrained double monophonic number.
Funding agency Grant number
NBHM NBHM/R.P.29/2015/Fresh/157
The second author research work was supported by National Board for Higher Mathematics, INDIA (Project No. NBHM/R.P.29/2015/Fresh/157).
Bibliographic databases:
Document Type: Article
Language: English
Citation: A. P. Santhakumaran, K. Ganesamoorthy, “Restrained double monophonic number of a graph”, Ural Math. J., 5:2 (2019), 55–63
Citation in format AMSBIB
\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:
    1. 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  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    Ural Mathematical Journal
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    References:28
     
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