1,870 research outputs found
On the diameter of dot-critical graphs
A graph G is -dot-critical (totaly -dot-critical) if is dot-critical (totaly dot-critical) and the domination number is . In the paper [T. Burtona, D. P. Sumner, Domination dot-critical graphs, Discrete Math, 306 (2006), 11-18] the following question is posed: What are the best bounds for the diameter of a -dot-critical graph and a totally -dot-critical graph with no critical vertices for ? We find the best bound for the diameter of a -dot-critical graph, where and we give a family of -dot-critical graphs (with no critical vertices) with sharp diameter for even
Total Domination Dot Critical and Dot Stable Graphs.
Two vertices are said to be identifed if they are combined to form one vertex whose neighborhood is the union of their neighborhoods. A graph is total domination dot-critical if identifying any pair of adjacent vertices decreases the total domination number. On the other hand, a graph is total domination dot-stable if identifying any pair of adjacent vertices leaves the total domination number unchanged. Identifying any pair of vertices cannot increase the total domination number. Further we show it can decrease the total domination number by at most two. Among other results, we characterize total domination dot-critical trees with total domination number three and all total domination dot-stable graphs
Domination changing and unchanging signed graphs upon the vertex removal
A subset S of V (ÎŁ) is a dominating set of ÎŁ if |Nâș(v) â© S| > |Nâ»(v) â© S| for all v â V â S. This article is to start a study of those signed graphs that are stable and critical in the following way: If the removal of an arbitrary vertex does not change the domination number, the signed graph will be stable. The signed graph, on the other hand, is unstable if an arbitrary vertex is removed and the domination number changes. Specifically, we analyze the change in the domination of the vertex deletion and stable signed graphs.Publisher's Versio
On the detectability of non-trivial topologies
We explore the main physical processes which potentially affect the
topological signal in the Cosmic Microwave Background (CMB) for a range of
toroidal universes. We consider specifically reionisation, the integrated
Sachs-Wolfe (ISW) effect, the size of the causal horizon, topological defects
and primordial gravitational waves. We use three estimators: the information
content, the S/N statistic and the Bayesian evidence. While reionisation has
nearly no effect on the estimators, we show that taking into account the ISW
strongly decreases our ability to detect the topological signal. We also study
the impact of varying the relevant cosmological parameters within the 2 sigma
ranges allowed by present data. We find that only Omega_Lambda, which
influences both ISW and the size of the causal horizon, significantly alters
the detection for all three estimators considered here.Comment: 11 pages, 9 figure
On the Number of Incipient Spanning Clusters
In critical percolation models, in a large cube there will typically be more
than one cluster of comparable diameter. In 2D, the probability of
spanning clusters is of the order . In dimensions d>6, when
the spanning clusters proliferate: for the spanning
probability tends to one, and there typically are spanning
clusters of size comparable to |\C_{max}| \approx L^4. The rigorous results
confirm a generally accepted picture for d>6, but also correct some
misconceptions concerning the uniqueness of the dominant cluster. We
distinguish between two related concepts: the Incipient Infinite Cluster, which
is unique partly due to its construction, and the Incipient Spanning Clusters,
which are not. The scaling limits of the ISC show interesting differences
between low (d=2) and high dimensions. In the latter case (d>6 ?) we find
indication that the double limit: infinite volume and zero lattice spacing,
when properly defined would exhibit both percolation at the critical state and
infinitely many infinite clusters.Comment: Latex(2e), 42 p, 5 figures; to appear in Nucl. Phys. B [FS
Energy dissipation prediction of particle dampers
This paper presents initial work on developing models for predicting particle dampers (PDs) behaviour using the Discrete Element Method (DEM). In the DEM approach, individual particles are typically represented as elements with mass and rotational inertia. Contacts between particles and with walls are represented using springs, dampers and sliding friction interfaces. In order to use DEM to predict damper behaviour adequately, it is important to identify representative models of the contact conditions. It is particularly important to get the appropriate trade-off between accuracy and computational efficiency as PDs have so many individual elements. In order to understand appropriate models, experimental work was carried out to understand interactions between the typically small (1.5â3 mm diameter) particles used. Measurements were made of coefficient of restitution and interface friction. These were used to give an indication of the level of uncertainty that the simplest (linear) models might assume. These data were used to predict energy dissipation in a PD via a DEM simulation. The results were compared with that of an experiment
Percolation on self-dual polygon configurations
Recently, Scullard and Ziff noticed that a broad class of planar percolation
models are self-dual under a simple condition that, in a parametrized version
of such a model, reduces to a single equation. They state that the solution of
the resulting equation gives the critical point. However, just as in the
classical case of bond percolation on the square lattice, self-duality is
simply the starting point: the mathematical difficulty is precisely showing
that self-duality implies criticality. Here we do so for a generalization of
the models considered by Scullard and Ziff. In these models, the states of the
bonds need not be independent; furthermore, increasing events need not be
positively correlated, so new techniques are needed in the analysis. The main
new ingredients are a generalization of Harris's Lemma to products of partially
ordered sets, and a new proof of a type of Russo-Seymour-Welsh Lemma with
minimal symmetry assumptions.Comment: Expanded; 73 pages, 24 figure
An introduction to cosmology
Cosmology is becoming an important tool to test particle physics models. We
provide an overview of the standard model of cosmology with an emphasis on the
observations relevant for testing fundamental physics.Comment: Lectures given at the CERN Latin-American School of High Energy
Physics CLASHEP 2015, Ibarra, Ecuador. Submitted for publication in a CERN
Yellow Repor
Communication Network Among Campus Sustainability Influencers
Systems of all types require efficient communication between its parts and units in order to be successful and e ective. It is thus important to understand a systems units in order to better advance its operations. In this study, we look at Loyola Marymount University (LMU) as a systematic organization in regards to the universitys execution of its environmental sustainability endeavors. This approach allows for the identification of the path by which important environmental sustainability information is communicated, is learned, and is acted upon at LMU. Through various network centrality measurements, I will develop a visual representation of the communication network between individuals on LMU\u27s campus who have an interest and play a role in the development and advancement of environmental sustainability practices and policies on campus. Moreover, an analytical understanding of this network of information transference will provide insight into the decision-making, implementation, and management that affects the e orts to reduce LMU\u27s campus carbon footprint
Strong Dependencies between Software Components
Component-based systems often describe context requirements in terms of
explicit inter-component dependencies. Studying large instances of such
systems?such as free and open source software (FOSS) distributions?in terms of
declared dependencies between packages is appealing. It is however also
misleading when the language to express dependencies is as expressive as
boolean formulae, which is often the case. In such settings, a more appropriate
notion of component dependency exists: strong dependency. This paper introduces
such notion as a first step towards modeling semantic, rather then syntactic,
inter-component relationships. Furthermore, a notion of component sensitivity
is derived from strong dependencies, with ap- plications to quality assurance
and to the evaluation of upgrade risks. An empirical study of strong
dependencies and sensitivity is presented, in the context of one of the
largest, freely available, component-based system
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