RESTRICTED DOMINATION PROBLEMS ON GRAPHS

Graph Theory is widely used to develop a model for solving many real life problems of Social Science, Computer Science, Linguistics, Physics, Chemistry, Biology and Mathematics related topics. However, these types of graph problems are usually NP-hard and so there is no efficient algorithm for solving them unless P = NP. In this book, restricted form of graphs is used to overcome and solve this hardness of the problems. The aim of this research is to study of some important variations of domination problems in various intersection graphs, which is one of the major branches of modern graph theory. In the first part of the research work, the construction of algorithms in restricted forms such as 2-tuple domination problems on trapezoid graphs and Circular arc graphs, signed star domination number on proper interval graphs, Signed edge domination number of interval graphs, Roman domination on acyclic Permutation graphs have been discussed.Finally, the two new variations, ¿Signed Roman Star Edge Domination Number¿ and ¿Edge Roman Star Domination Number¿ of Roman domination have been introduced and their various boundary values in different graphs have been computed.