Search

Let G = (V (G);E(G)) be a graph, γt(G). Let ooir(G) be the total domination and OO-irredundance number of G, respectively. A total dominating set S of G is called a total perfect code if every vertex in V (G) is adjacent to exactly one vertex of S. In this paper, we show that if G has a total perfect code, then γt(G) = ooir(G). As a consequence, we determine the value of ooir(G) for some classes of graphs. Finally, we prove some new bounds for the total subdivision number. [ABSTRACT FROM AUTHOR]

In this paper, we show that for all v ≡ 1 (mod 3), there exists a super-simple ( v , 4 , 2 ) directed design. Also, we show that for these parameters there exists a super-simple ( v , 4 , 2 ) directed design whose each defining set has at least a half of the blocks. [ABSTRACT FROM AUTHOR]