RESTRAINED DOUBLE MONOPHONIC NUMBER OF A GRAPH

A.P. Santhakumaran     (Department of Mathematics, Hindustan Institute of Technology and Science, Chennai - 603 103, India)
K. Ganesamoorthy     (Department of Mathematics, Coimbatore Institute of Technology, Coimbatore - 641 014, India)

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 \(dm_{r}(G)\). The restrained double monophonic number of certain classes graphs are determined. It is shown that for any integers \(a,\, b,\, c\) with \(3 \leq a \leq b \leq c\), there is a connected graph \(G\) with \(m(G) = a\), \(m_r(G) = b\) and \(dm_{r}(G) = c\), where \(m(G)\) is the monophonic number and \(m_r(G)\) is the restrained monophonic number of a graph \(G\).


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References


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DOI: http://dx.doi.org/10.15826/umj.2019.2.005

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