In this paper we initialize the study of independent domination in directed graphs. We show that an independent dominating set of an orientation of a graph is also an independent dominating set of the underlying graph, but that the converse is not true in general. We then prove existence and uniqueness theorems for several classes of digraphs including orientations of complete graphs, paths, tr...

‎A Roman dominating function (RDF) on a graph G=(V,E) is a function  f : V → {0, 1, 2}  such that every vertex u for which f(u)=0 is‎ ‎adjacent to at least one vertex v for which f(v)=2‎. ‎An RDF f is called‎‎an outer independent Roman dominating function (OIRDF) if the set of‎‎vertices assigned a 0 under f is an independent set‎. ‎The weight of an‎‎OIRDF is the sum of its function values over ...

Abstract A set of vertices in a graph is dominating if every vertex or adjacent to . If, addition, an independent set, then set. The domination number the minimum cardinality , while We prove that for all integers it holds connected ‐regular graph, with equality and only result was previously known This affirmatively answers question Babikir Henning.

Supergrid graphs are derived by computing stitch paths for computerized embroidery machines. In the past, we have studied Hamiltonian-related properties of supergrid and their subclasses graphs. this paper, propose a generalized graph class called extended Extended include grid graphs, diagonal triangular as study problems domination independent on A dominating set is subset vertices it, such t...