Edge Monophonic Domination Number of Graphs

Authors

  • Arul Paul Sudhahar Department of Mathematics, Rani Anna Govt.College(W), Tirunalveli-620 008, Tamilnadu, India.
  • MOHAMMED ABDUL KHAYYOOM Department of Higher Secondary Education, Govt.Vocational HSS Omanoor-673 645, Kerala,India

DOI:

https://doi.org/10.24297/jam.v11i10.812

Keywords:

Edge monophonic number, monophonic domi- nation number, edge monophonic domination number.

Abstract

In this paper the concept of edge monophonic domination num-ber of a graph is introduced.A set of vertices D of a graph G is edge mono-phonic domination set (EMD set) if it is both edge monophonic set and adomination set of G.The edge monophonic domination number (EMD num- ber) of G, me(G) is the cardinality of a minimum EMD set. EMD number of some connected graphs are realized.Connected graphs of order n with EMD number n are characterised.It is shown that for any two integers p and q such that 2 p q there exist a connected graph G with m(G) = p and me(G) = q.Also there is a connected graph G such that (G) = p;me(G) = q and me(G) = p + q

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Author Biographies

Arul Paul Sudhahar, Department of Mathematics, Rani Anna Govt.College(W), Tirunalveli-620 008, Tamilnadu, India.

Assistant Professor,

Department of Mathematics,Rani Anna Govt.College(W),
Tirunalveli-620 008, Tamilnadu, India.

MOHAMMED ABDUL KHAYYOOM, Department of Higher Secondary Education, Govt.Vocational HSS Omanoor-673 645, Kerala,India

Hsst in Mathemetics

Department of Higher Secondary Education, Govt.Vocational HSS
Omanoor-673 645, Kerala,India

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Published

2016-01-16

How to Cite

Sudhahar, A. P., & KHAYYOOM, M. A. (2016). Edge Monophonic Domination Number of Graphs. JOURNAL OF ADVANCES IN MATHEMATICS, 11(10), 5781–5785. https://doi.org/10.24297/jam.v11i10.812

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