On Existence Problem Of Total Domination Vertex Critical Graphs

For any total domination vertex critical graphs G, so that G m is the total domination number,△is the maximum degree of G, then G has at least△+m points. Now consider for any△and m, Whether there is a total domination vertex critical graphs G with total domination m, maximum degree△, minimum degree2and just△+m control points.The front part is research about this problem, refer to Sohn, Kim, Kwon, Lee’s article [On the total domination critical graphs, Discrete Applied Mathe-matics159(2011)46-52], and add some my own proof. First I elaborated the properties meet the control point m+G of the critical graph, The△and m re-spectively, classification discussion.At last,I prove the situation which is m=5,△=5and part of m=5,△=7。...