Two new domination parameters for a connected graph G: the weakly convex domination number of G and the convex domination number of G are introduced. Relations between these parameters and the otherâ€¦ (More)

The distance dG(u, v) between two vertices u and v in a connected graph G is the length of the shortest uv-path in G. A uv-path of length dG(u, v) is called uv-geodesic. A set X is convex in G ifâ€¦ (More)

For a connected graph G = (V,E), a set D âŠ† V (G) is a dominating set of G if every vertex in V (G)âˆ’D has at least one neighbour in D. The distance dG(u, v) between two vertices u and v is the lengthâ€¦ (More)

The weakly connected domination subdivision number sdÎ³w(G) of a connected graph G is the minimum number of edges which must be subdivided (where each edge can be subdivided at most once) in order toâ€¦ (More)

Given an ordered partition Î = {P1, P2, ..., Pt} of the vertex set V of a connected graph G = (V,E), the partition representation of a vertex v âˆˆ V with respect to the partition Î is the vectorâ€¦ (More)

The domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be subdivided k times to increase theâ€¦ (More)