Monophonic eccentric domination in graphs

Abstract

This thesis entitled quotMONOPHONIC ECCENTRIC DOMINATION IN GRAPHSquot consists of seven chapters. In Chapter 1, we collect the basic definitions, which are needed for the subsequent chapters. Let G be a non-trivial finite undirected connected graph without loops and multiple edges. For basic graph theoretic terminology, we refer to (Bondy and Murty 1976), (Buckley and Harary 1990), (Chartrand and Zhang 2006) and (Harary 1969). newlineIn Chapter 2, we introduce the concept of monophonic eccentric dominating sets and the monophonic eccentric domination number of a graph. A set S C V in a graph G is a monophonic eccentric dominating set if every vertex in V S has a monophonic eccentric vertex in S. The monophonic eccentric domination number ynie (G) is the cardinality of a minimum monophonic eccentric dominating set of G. Some properties of monophonic eccentric dominating sets are investigated. Also, we determine the bounds of the monophonic eccentric domination number and find the same for some standard graphs. newlineIn Chapter 3, we establish bounds for the monophonic eccentric domination number of the corona product of two graphs. Also, exact values of the monophonic eccentric domination number of corona product of some standard graphs are determined. newlineIn Chapter 4, we introduce the concept of connected monophonic eccentric dominating sets and the connected monophonic eccentric domination number of a graph newline newline