Some Results on Inverse Domination Parameters in Graphs

Abstract

A graph G = (v;E), mean a finite undirected graph have neither loops nor parallel edges. For graph theoretic terminology refer to Gary Chartrand and Ping Zhang [3].In Chapter 1, introduction to this thesis are provided. In this chapter, some basic definitions,notions, the concept of domination are collected and discussed with its applications for real life problems. A review of established results is also provided. Domination is a fast growing area of research in Graph Theory and it is developing steadily. Increased interest of research in the field of domination is partly explained by its applications to ad hoc networks, distributed computing, social networks and web graphs. An excellent treatment of fundamentals on domination in graphs is given by Haynes et al. [8, 9]. This thesis is focused on domination theory and the main objective of the study is to obtain new results for various domination parameters. The chapter 2, discusses the notions of inverse domination concept in newlinegraphs with the help of some interesting well known graphs. Also, it contains proofs for new results established. The chapter 3, provides new results for Pair domination concept and the inverse case of Pair domination. In chapter 4, particular cases of Fair domination in graphs, especially for k = 1 and k = 2 in some classes of graphs, are discussed and provided some results The chapter 5, deals with the concept of inverse case of Fair domination number in a graph . The new results obtained relating to inverse fair domination, for some standard graphs are presented in this chapter. We have explored several possibilities for future research in basic results and problems. newline newline