Domination and Distance k-domination stable graphs

In the first chapter of this book, we provide basic definitions and theorems which are used in the subsequent chapters. In the second chapter, we define domination polynomial, domination root and d- number of a graph. Moreover, we introduce d- stable and d-unstable graphs. Domination polynomial of some graphs and domination polynomial of square of some graphs are provided. Bounds for domination roots of some graphs are included. Examples of some d- stable and d-unstable graphs are included. Chapter 3 considers the study of distance k- domination polynomial, distance k-domination root and d k number of a graph. We have also discussed d k stable and d k unstable graphs. Chapter 4 deals with some general properties of domination and distance k domination polynomials.

Autorentext

Dr. Anil Kumar V. is an Associate Professor of Mathematics, Universityof Calicut, India. He earned a Ph.D in Mathematics from Universityof Kerala, India in 1997, working in area of graph theory. He remainsactive in research in graph theory.Shyama M.P. is an Assistant Professor of Mathematics, Malabar ChristianCollege, Kerala, India.