Study Of Domination-related Parameters In Graphs

Domination-related parameters theory has increasingly developed an active re-searching area in graph theory and its study has an important significant. There are close relationships between problems domination-related parameters and problems from other fields,such as combinational optimization, theoretical computer science and so on. Domination-related parameters have direct applications in many practical problems in daily life, such as in facility location,communication system,monitor system and army arrangement and so on. Basing on a differently practical background and dom-ination, researchers put forward to many domination-related parameters,such as signed domination,k-distance domination,signed edge domination,domatic-domination. In this paper,we mainly study inverse roman domination number, signed edge distance-k-domination number and signed clique edge-domatic number. There are four chapters to this paper.In chapter 1, we mainly introduce some domination-related concepts and defini-tions. The research status about this paper are introduced and mainly results of this paper are listed.In chapter 2, we mainly study an exact value of inverse roman domination number for some special graphs such as paths and roads and prove bounds of inverse roman domination number for any graph.In chapter 3,we mainly research signed edge distance-k-domination number on some simple graphs,especially k= 1 and obtain its bounds.In chapter 4,Basing on the theory significant and real background of signed edge-domatic number,we generalize signed edge-domatic number to signed clique edge-domatic number. We mainly discuss the problem of signed edge-domatic number-signed clique edge-domatic number with the concept of the clique number. We prove that the signed clique edge-domatic number on this class of graphs and the signed clique edge-domatic number of their maximal clique Kω have some relations and we obtain the signed clique edge-domatic number for any graphs.