Split Domination Vertex Critical and Edge Critical Graphs

Majority domination vertex critical graphs

This paper deals the graphs for which the removal of any vertex changes the majority domination number of the graph. In the following section, how the removal of a single vertex fromG can change the majority domination number is surveyed for trees. Characterisation of V + M (G) and V − M (G) are determined.

Nonsplit Domination Edge Critical Graphs

A set of vertices S is said to dominate the graph G if for each v / ∈ S, there is a vertex u ∈ S with u adjacent to v. The minimum cardinality of any dominating set is called the domination number of the graph G and is denoted by γ(G). A dominating set D of a graph G = (V,E) is a nonsplit dominating set if the induced graph 〈V − D〉 is connected. The nonsplit domination number γns(G) of the grap...

Majority Domination Edge Critical Graphs

This paper deals the graphs for which the removal of any edge changes the majority domination number of the graph. γM -critical edges, γM -redundant edges, γM -durable graphs and γM -critical graphs are studied. Further, majority domination critical edges and majority domination critical graphs are characterized.

Vertex Domination Critical in Circulant Graphs

Domination parameters and edge-removal-critical graphs

For any of the basic domination parameters ir, , i, , or IR, we study graphs for which increases whenever an edge is removed ( -ER-critical graphs) and graphs for which decreases whenever an edge is removed ( −-ER-critical graphs). The latter case is only possible if = i or (perhaps) = ir. We give examples of classes of -ER-critical graphs for an upper domination parameter and characterize thes...