Asian Journal of Mathematics and Computer Research
 

Asian Journal of Mathematics and Computer Research, ISSN No. : 2395-4205 (Print), 2395-4213 (Online), Vol.: 23, Issue.: 4

Original Research Article

TOTAL RESTRAINED EDGE MONOPHONIC DOMINATION NUMBER M OF A GRAPH

 

P. ARUL PAUL SUDHAHAR1, M. LITTLE FLOWER2* AND E. EBIN RAJA MERLY3

1Department of Mathematics, Rani Anna Govt. College (W), Tirunelveli – 627 008, Tamil Nadu, India.

2Department of Mathematics, Nanjil Catholic College of Arts and Science, Kaliyakkavilai – 629 153, Tamil Nadu, India.

3Department of Mathematics, N. M. Christian College, Marthandam – 629 165, Tamil Nadu, India.

Abstracts

In this paper the concept of total restrained edge monophonic domination number M of a graph G is introduced. For a connected graph G = (V,E) of order at least two, a  total restrained edge monophonic dominating set M of a graph G is a restrained edge monophonic dominating set M such that the subgraph induced by M has no isolated  vertices. A total restrained edge monophonic dominating set of cardinality   is called a  - set of G . It is shown that if p and k are positive integers such that 3≤ k ≤ p there exists a connected graph G of order P such that k . Also For any positive integers 3 < a < b < c < d , there exists a connected graph G such that me(G) = a,  and = d.

Keywords :

Restrained edge monophonic dominating set; restrained edge monophonic domination number; total restrained edge monophonic dominating set; total restrained edge monophonic domination number.