Proper dominating functions of graphs
James Hallas, Maria Talanda-Fisher, Ping Zhang · Contributions to Mathematics · 2020
for every two adjacent vertices x and y of G, then f is a proper dominating function of G. Sufficient conditions are obtained under which a graph has a proper dominating function and sufficient conditions are obtained under which a graph does not have a proper dominating function.For certain classes of graphs, all those members possessing a proper dominating function are determined.