THE SEMI-TOTAL MONOPHONIC DOMINATION NUMBER OF A GRAPH

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Published: 2019-06-14

Page: 88-94


P. ARUL PAUL SUDHAHAR *

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

A. J. BERTILLA JAUSHAL

Department of Mathematics, Nanjil Catholic College of Arts and Science, Manonmaniam Sundaranar University, Kaliyakkavilai – 629 153, Kanyakumari District, Tirunelveli – 627 012, Tamil Nadu, India.

*Author to whom correspondence should be addressed.


Abstract

In this paper the concept of semi-total monophonic domination number of a graph is introduced. A set of vertices  of a graph  is called a total monophonic set if  is a monophonic set and its induced subgraph has no isolated vertices. The minimum cardinality of all total monophonic sets of  is called the total monophonic number and is denoted by.  A set of vertices  in  is called a monophonic dominating set if  is both a monophonic set and a dominating set. The minimum cardinality of a monophonic dominating set of  is its monophonic domination number and is denoted by . A monophonic dominating set of size  is said to be a  set. A set  of vertices in a graph  with no isolated vertices is said to be a semi-total monophonic set of   if it is a monophonic set of   and every vertex in  is within distance 2 of another vertex of . The semi-total monophonic AMS Subject classification:  05C12 number, denoted by , is the minimum cardinality of a semitotal monophonic dominating set of .

Keywords: Monophonic dominating set, monophonic domination number, semi-total monophonic dominating set, semi-total monophonic domination number


How to Cite

SUDHAHAR, P. A. P., & JAUSHAL, A. J. B. (2019). THE SEMI-TOTAL MONOPHONIC DOMINATION NUMBER OF A GRAPH. Asian Journal of Mathematics and Computer Research, 26(2), 88–94. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/4607

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