The Inverse Domination in Semi-total Block Graphs
K. Ameenal Bibi, R. Selvakumar · International Journal of Computer Applications · 2010
Let G = (V, E) be a simple, finite, undirected graph with V = n and E = m.Kulli introduced the new graph valued function namely the semi-total block graph of a graph G. Let B 1 = {u 1 ,u 2 ,...,u r , r 2} be a block of G. Then we say that the point u 1 and block B 1 are incident with each other, as are u 2 and B 1, u 3 and B 1 and so on.If two distinct blocks B 1 and B 2 are incident with a common cut point then they are called adjacent blocks.which any two points are either adjacent or the corresponding members of G are incident.The points and blocks of G are members of T band it is defined as the minimum cardinality taken over all the minimal dominating sets of T b (G).In this paper, we defined Inverse domination in semi-total block graphs.Let D be the minimum dominating set of T b (G).If (V B)-D contains a dominating set D' then D' is called the Inverse dominating set of T b (G).The Inverse domination number in semi-total block graph is denoted by '[T b (G)] and it is defined as the minimum cardinality taken over all the minimal Inverse dominating sets of T b (G).In this paper, many bounds on '[T b (G)] are attained and its exact values for some standard graphs are found.Its relationships with other parameters are investigated.Nordhaus-Gaddum type results are also obtained for this parameter.