A Note on Domatic Subdivision Stable Graphs
M. Yamuna, K. Karthika · Universal Journal of Applied Mathematics · 2014
A domatic partition of a graph G = ( V, E ) is a partition of V into disjoint sets V1, V2, ..., VK such that each Vi is a dominating set for G. A subdivision of a graph G is a graph resulting from the subdivision of edges in G. In this paper we discuss about the minimal properties of domatic subdivision stable graph and we show that every graph is an induced subgraph of a domatic subdivision stable graph. We discuss methods of generating new domatic subdivision stable graphs from existing domatic subdivision stable graphs using graph operations.