We study a probabilistic optimization model for graph-problems under vertex-uncertainty. We assume that any vertex vi of the input-graph G(V,E) has only a probability pi to be present in the final graph to be optimized (i.e., the final instance for the problem tackled will be only a sub-graph of the initial graph). Under this model, the original “deterministic” problem gives rise to a new (dete...

In the present work, we investigate decays of $B^{0}_{s} \rightarrow \phi\pi^{+}\pi^{-}$ and $B^{0} with final state interactions based on chiral unitary approach. $\pi^+\pi^-$ its coupled channels, study effects $\eta\eta$ channel in two-body for reproduction $f_{0}(980)$ state. Our results invariant mass distributions decay describe experimental data up to 1 GeV well, resonance contributions ...

Through a series of papers in the 1980’s, Bouchet introduced isotropic systems and the Tutte-Martin polynomial of an isotropic system. Then, Arratia, Bollobás, and Sorkin developed the interlace polynomial of a graph in [ABS00] in response to a DNA sequencing application. The interlace polynomial has generated considerable recent attention, with new results including realizing the original inte...

Let G be a simple connected graph of order n. Dcνe (G, i) the family vertex-edge dominating sets with cardinality i. The polynomial x) = is called domination where dcνe number vertex edge G. In this paper, we study some properties polynomials Gem Gn. Also obtain (Gn, and their coefficients. Also, find recursive formula, to derive

We present the rst truly polynomial-time approximation scheme (PTAS) for the minimum-cost k-vertex-(or, k-edge-) connected spanning subgraph problem for complete Euclidean graphs in R d : Previously it was known for every positive constant " how to construct in a polynomial time a graph on a superset of the input points which is k-vertex connected with respect to the input points, and whose cos...

We consider the two-variable interlace polynomial introduced by Arratia, Bollobás and Sorkin (2004). We develop two graph transformations which allow us to derive point-to-point reductions for the interlace polynomial. Exploiting these reductions we obtain new results concerning the computational complexity of evaluating the interlace polynomial at a fixed point. Regarding exact evaluation, we ...

The methodology of positioning graph vertices relative to each other to solve the problem of determining isomorphism of two undirected graphs is developed. Based on the position of the vertex in one of the graphs, it is determined the corresponding vertex in the other graph. For the selected vertex of the undirected graph, define the neighborhoods of the vertices are defined. Next, it is constr...

We consider the two-variable interlace polynomial introduced by Arratia, Bollobás and Sorkin (2004). We develop two graph transformations which allow us to derive point-to-point reductions for the interlace polynomial. Exploiting these reductions we obtain new results concerning the computational complexity of evaluating the interlace polynomial at a fixed point. Regarding exact evaluation, we ...

The problem of finding a minimum weight k-vertex connected spanning subgraph is considered. For k ≥ 2, this problem is known to be NP-hard. Combining properties of inclusion-minimal k-vertex connected graphs and of k-out-connected graphs (i.e., graphs which contain a vertex from which there exist k internally vertex-disjoint paths to every other vertex), we derive polynomial time approximation ...

Some special cases such as t-designs (g constant), partial Steiner systems (g constant and equal to 1), degree sequences of r-uniform hypergraphs (t = 1) and some related problems such as f -vectors of pure simplicial complexes [23, 26, 20] have received much attention during the last three decades. Yet we know very little about the problem. We do not even know whether or not it is NP-complete....