A set S ⊂ V is a dominating set of a graph G = (V,E) if every vertex v ∈ V which does not belong to S has a neighbour in S. The domination number γ(G) of the graph G is the minimum cardinality of a dominating set in G. A dominating set S is a γ-set in G if |S| = γ(G). Some graphs have exponentially many γ-sets, hence it is worth to ask a question if a γ-set can be obtained by some transformatio...

Introduction: In most BCI articles which aim to separate movement imaginations, µ and &beta frequency bands have been used. In this paper, the effect of presence and absence of &gamma band on performance improvement is discussed since movement imaginations affect &gamma frequency band as well. Methods: In this study we used data set 2a from BCI Competition IV. In this data set, 9 healthy sub...

let $r$ be a commutative ring with zero-divisor set $z(r)$. the total graph of $r$, denoted by$t(gamma(r))$, is the simple (undirected) graph with vertex set  $r$ where two distinct vertices areadjacent if their sum lies in $z(r)$.this work considers minimum zero-sum $k$-flows for $t(gamma(r))$.both for $vert rvert$ even and the case when $vert rvert$ is odd and $z(g)$ is an ideal of $r$it is s...

The internal/external synchrotron shock scenario has proved very successful in interpreting the key observations about gamma–ray bursts. There still remains, however, some big uncertainties. The hottest issue concerns the nature of the progenitor, but there are also other problems concerning the global energetics, coupled with the issue of the degree of the collimation of the fireball. To be ef...

In this paper, we study deformations of complex structures on Lie algebras and its associated Dolbeault cohomology classes. A complete deformation is constructed in a way similar to the Kuranishi family. The extension isomorphism shown be valid case. As an application, prove that given family left invariant $\{M_t\}_{t\in B}$ compact manifold $M=(\Gamma\setminus G, J)$ where $G$ group, $\Gamma$...

A paired dominating set $P$ is a with the additional property that has perfect matching. While maximum cardainality of minimal in graph $G$ called upper domination number $G$, denoted by $\Gamma(G)$, cardinality $\Gamma_{pr}(G)$. By Henning and Pradhan (2019), we know $\Gamma_{pr}(G)\leq 2\Gamma(G)$ for any without isolated vertices. We focus on graphs satisfying equality $\Gamma_{pr}(G)= 2\Gam...

 Let $R$ be a commutative ring and $M$ be an $R$-module with $T(M)$ as subset, the set of torsion elements. The total graph of the module denoted by $T(Gamma(M))$, is the (undirected) graph with all elements of $M$ as vertices, and for distinct elements $n,m in M$, the vertices $n$ and $m$ are adjacent if and only if $n+m in T(M)$. In this paper we study the domination number of $T(Gamma(M))$ a...