p-vertex dominating graph andp-vertex domination number
L. Nallasivan · Journal of Information and Optimization Sciences · 2014
A p-vertex dominating graph is a finite, simple and connected graph G with exactly p-vertices adjacent to all the vertices of G. We characterize 1-vertex dominating graph. We construct 1-vertex dominating graphs with maximum number of edges and prove that they are hamiltonian, 2-connected, triple connected and 1-hamiltonian. More over we define a 1-vertex dominating set D1v and the 1-vertex domination number γ1v (G) of a graph G. Also we find the 1-vertex domination number for some graphs.