The Domination And The Connected Domination On The Graph

Because the search on the domination numbers is more and more attached importance to people get more deeply aware of it and put forward many domination parameters , such as itotal domination number , minus domination number , negative domination number, and so on. Those types of domination number play an important role in structure of graphs. And the decision problems corresponding to those are NP?complete or NP?hard. Therefore, it's very necessary to estimate bands of those.In this paper, we mainly survey relationship between domination numbers and connected domination numbers in some graphs and problem on qualities and connected domination number in some graph, [3] describes structure of some treeswhich satisfies . Actually, there are many trees which do not satisfy thiscondition. Then we want to discuss bound of ?more deeply in trees and obtaintwo better conclusions :(l)For any tree T , which is the best bound . (2) For any connected graph G if there is at more one cycle , than And by proofing conclusion 2, we obtain findings on unique smallest domination set.In resolving problem on qualities of some graphs in which describes unicyclic graph. I will give the description of disjointing double cyclic graph .