Search results for "VERTEX"
showing 10 items of 225 documents
Adjacency matrices of random digraphs: singularity and anti-concentration
2017
Let ${\mathcal D}_{n,d}$ be the set of all $d$-regular directed graphs on $n$ vertices. Let $G$ be a graph chosen uniformly at random from ${\mathcal D}_{n,d}$ and $M$ be its adjacency matrix. We show that $M$ is invertible with probability at least $1-C\ln^{3} d/\sqrt{d}$ for $C\leq d\leq cn/\ln^2 n$, where $c, C$ are positive absolute constants. To this end, we establish a few properties of $d$-regular directed graphs. One of them, a Littlewood-Offord type anti-concentration property, is of independent interest. Let $J$ be a subset of vertices of $G$ with $|J|\approx n/d$. Let $\delta_i$ be the indicator of the event that the vertex $i$ is connected to $J$ and define $\delta = (\delta_1, …
Diferratricarbaboranes of thesubcloso-[(η5-C5H5)2Fe2C3B8H11] Type, the First Representatives of the 13-Vertex Dimetallatricarbaborane Series
2003
Treatment of the [2-Cp-9-tBuNH-closo-2,1,7,9-FeC 3 B 8 H 1 0 ] (1) ferratricarbollide (Cp = η 5 -C 5 H 5 -) with Na + C 1 0 H 8 - in 1,2-dimethoxyethane (DME) at room temperature produced an air-sensitive transient anion with a tentatively identified nido-[tBUNH-CpFeC 3 B 8 H 1 0 ] 2 - constitution. In-situ reaction of this low-stability ion with [CpFe(CO) 2 I] or [CpFe(CO) 2 ] 2 generated three violet diferratricarbaboranes identified as paramagnetic subcloso complexes [4,5-Cp 2 - -4,5,1,6,7-Fe 2 C 3 B 8 H 1 1 ] (2; yield 2%), [4,5-Cp 2 - -4,5,1,7,12-Fe 2 C 3 B 8 H 1 1 ] (3; yield 2%), and [7-tBuNH-4,5-Cp 2 - -4,5,1,7,12-Fe 2 C 3 B 8 H 1 0 ] (4; yield 14%). These first representatives of t…
Combined column-and-row-generation for the optimal communication spanning tree problem
2018
Abstract This paper considers the exact solution of the optimal communication spanning tree problem (OCSTP), which can be described as follows: Given an undirected graph with transportation costs on every edge and communication requirements for all pairs of vertices, the OCSTP seeks for a spanning tree that minimizes the sum of the communication costs between all pairs of vertices, where the communication cost of a pair of vertices is defined as their communication requirement multiplied by the transportation cost of the unique tree path that connects the two vertices. Two types of compact formulations for OCSTP were presented in the literature. The first one is a four-index model based on …
Generalized Molecular Descriptors Derived From Event-Based Discrete Derivative.
2016
In the present study, a generalized approach for molecular structure characterization is introduced, based on the relation frequency matrix (F) representation of the molecular graph and the subsequent calculation of the corresponding discrete derivative (finite difference) over a pair of elements (atoms). In earlier publications (22- 24), an unique event, named connected subgraphs, (based on the Kier-Hall's subgraphs) was systematically employed for the computation of the matrix F. The present report is a generalization of this notion, in which eleven additional events are introduced, classified in three categories, namely, topological (terminal paths, vertex path incidence, quantum subgrap…
Miscellaneous Graph Preliminaries
2020
Summary This article contains many auxiliary theorems which were missing in the Mizar Mathematical Library [2] to the best of the author’s knowledge. Most of them regard graph theory as formalized in the GLIB series (cf. [8]) and most of them are preliminaries needed in [7] or other forthcoming articles.
A Hard X-Ray View of Scorpius X-1 with INTEGRAL : Nonthermal Emission?
2006
We present here simultaneous INTEGRAL/RXTE observations of Sco X-1, and in particular a study of the hard X-ray emission of the source and its correlation with the position in the Z-track of the X-ray color-color diagram. We find that the hard X-ray (above about 30 keV) emission of Sco X-1 is dominated by a power-law component with a photon index of ~3. The flux in the power-law component slightly decreases when the source moves in the color-color diagram in the sense of increasing inferred mass accretion rate from the horizontal branch to the normal branch/flaring branch vertex. It becomes not significantly detectable in the flaring branch, where its flux has decreased by about an order of…
Improving the local vertex invariants in alkane graphs through a standard molecular orbital approach
2007
Abstract In this work, novel topological indices are introduced by the application of algorithms based on molecular orbital theory. Actually, the novel indices are obtained by computing new values of the local vertex invariants (LOVIs) in alkane graphs. The most significant result is the dramatic increase in the predictive capability achieved with the topological charge indices weighted according the new LOVIs’ values in the prediction of four key properties in the set of octane isomers, namely heat of atomization, molar refraction, heat of vaporization and boiling point.
Stepwise formation of a pentanuclear Ni4Cu heterometallic complex exhibiting a vertex-sharing defective double-cubane core and diphenoxo- and phenoxo…
2013
Sequential reaction of a N5O3 octadentate tripodal ligand with Ni(2+) and subsequently with Cu(2+) and azide ligand afforded the first example of a heterobridged (phenoxo/μ(1,1)-azido) pentanuclear heterometallic (Ni4Cu) compound, which exhibits a centrosymmetric vertex-sharing defective double-cubane structure. The study of the magnetic properties reveals that the compound shows ferromagnetic interaction interactions, leading to an S = 9/2 spin ground state. Density functional theory calculations on the X-ray structure and model compounds predict ferromagnetic interactions through the magnetic exchange pathways involving each couple of metal ions.
Measurement of the lifetime of tau-lepton
1996
The tau lepton lifetime is measured with the L3 detector at LEP using the complete data taken at centre-of-mass energies around the Z pole resulting in tau_tau = 293.2 +/- 2.0 (stat) +/- 1.5 (syst) fs. The comparison of this result with the muon lifetime supports lepton universality of the weak charged current at the level of six per mille. Assuming lepton universality, the value of the strong coupling constant, alpha_s is found to be alpha_s(m_tau^2) = 0.319 +/- 0.015(exp.) +/- 0.014 (theory). The tau lepton lifetime is measured with the L3 detector at LEP using the complete data taken at centre-of-mass energies around the Z pole resulting in τ τ =293.2 ± 2.0 (stat) ± 1.5 (syst) fs . The c…
Neighbor-Distinguishing k-tuple Edge-Colorings of Graphs
2009
AbstractThis paper studies proper k-tuple edge-colorings of graphs that distinguish neighboring vertices by their sets of colors. Minimum numbers of colors for such colorings are determined for cycles, complete graphs and complete bipartite graphs. A variation in which the color sets assigned to edges have to form cyclic intervals is also studied and similar results are given.