A set D of vertices in a graph G(V, E) is a dominating set of G, if every vertex of V not in D is adjacent to at least one vertex in D. A dominating set D of G(V, E)is a k – fair dominating set of G, for | New parameters on inverse domination International Journal of Mechanical Engineering and Technology IJMET Volume 10 Issue 03 March 2019 pp. 1111-1116. Article ID IJMET_10_03_113 Available online at http ijmet JType IJMET amp VType 10 amp IType 3 ISSN Print 0976-6340 and ISSN Online 0976-6359 IAEME Publication Scopus Indexed NEW PARAMETERS ON INVERSE DOMINATION Jayasree T G Adi Shankara Institute of Engineering and Technology Kalady Kerala. Radha Rajamani Iyer Department of Mathematics Amrita School of Engineering Coimbatore Amrita Viswa Vidyapeetham India. ABSTRACT A set D of vertices in a graph G V E is a dominating set of G if every vertex of V not in D is adjacent to at least one vertex in D. A dominating set D of G V E is a k fair dominating set of G for 1 if every vertex in V D is adjacent to exactly k vertices in D. The k fair domination number of G is the minimum cardinality of a k fair dominating set. In this article we define the inverse of the k fair domination number and try to find it for some class of graphs. Key words Fair Domination Inverse Domination Inverse of k-fd set. Mathematics Subject Classification 05C69. Cite this Article Jayasree T G and Radha Rajamani Iyer New Parameters on Inverse Domination International Journal of Mechanical Engineering and Technology 10 3 2019 pp. 1111-1116. http IJMET JType IJMET amp VType 10 amp IType 3 1. INTRODUCTION Let G V E be a simple graph with vertex set V G and edge set E G . The order and size of G are denoted by n and m respectively. For graph theoretic terminology we refer to Gary Chartrand and Ping Zhang 10 and Haynes et al. 11 12 . For any vertex the open neighborhood N v is the set and the closed neighborhood N v is the set . For any and . A set D of vertices in a graph G V E is a dominating set of G if every vertex of V not in D is adjacent to at least one vertex in D. Let D be a minimum dominating set of G. If V - D contains a dominating set say D .
