An independent dominating set of the simple graph G=(V,E) is a vertex subset that both and in G. The domination polynomial G Di(G,x)=∑Ax|A|, summed over all subsets A⊆V. A root Di(G,x) called an independence root. We investigate polynomials some generalized compound graphs. As consequence, we construct graphs whose roots are real. Also, consider related to paths study number their sets.

During the last thirty years, the concept of domination in graphs has generated an impressive interest. A recent bibliography on the subject contains more than 1200 references and the number of new definitions is continually increasing. Rather than trying to give a catalogue of all of them, we survey the most classical and important notions (as independent domination, irredundant domination, k-...

control of three phase inverters has been an important issue in recent years. this paper proposes active disturbance rejection control (adrc) scheme for controlling three phase inverters. the main advantage of adrc that motivated us for using this controller for inverter is that it is model independent.  this controller is used in a double loop structure including an inner current loop and oute...

For a graphical property P and a graph G, we say that a subset S of the vertices of G is a P-set if the subgraph induced by S has the property P. Then the P-domination number of G is the minimum cardinality of a dominating P-set and the P-independence number the maximum cardinality of a P-set. We show that several properties of domination, independent domination and acyclic domination hold for ...

For a graphical property P and a graph G, we say that a subset S of the vertices of G is a P-set if the subgraph induced by S has the property P. Then the P-domination number of G is the minimum cardinality of a dominating P-set and the P-independence number the maximum cardinality of a P-set. We show that several properties of domination, independent domination and acyclic domination hold for ...

The k-domination number γk(G) of a simple, undirected graph G is the order of a smallest subset D of the vertices of G such that each vertex of G is either in D or adjacent to at least k vertices in D. In 2010, the conjecture-generating computer program, Graffiti.pc, was queried for upperbounds on the 2-domination number. In this paper we prove new upper bounds on the 2-domination number of a g...