scholarly journals Induced H-Packing k-Partition Problem in Certain Networks

2019 ◽  
Vol 8 (3) ◽  
pp. 1003-1010
Keyword(s):  
Independent Set ◽  
The Other ◽  
Partition Problem ◽  
Partition Number ◽  
Crossed Cube

A collection = {H1 ,H2 ,..., Hr } of induced sub graphs of a graph G is said to be sg-independent if (i) V(Hi ) V(Hj )= , i j, 1≤ i, j≤ r and (ii) no edge of G has its one end in Hi and the other end in Hj , i j, 1≤ i, j≤ r. If Hi H, ∀ i, 1≤ i ≤r, then is referred to as a H-independent set of G. Let be a perfect or almost perfect H-packing of a graph G. Finding a partition of such that is Hindependent set, ∀ i, 1 ≤ i ≤ k, with minimum k is called the induced H-packing kpartition problem of G. The induced H-packing k-partition number denoted by ipp(G,H) is defined as ipp(G,H) = min (G,H) where the minimum is taken over all H-packing of G. In this paper we obtain the induced H-packing k-partition number for Enhanced hypercube, Augmented Cubes and Crossed Cube networks where H is isomorphic to and .

Exact Equations for the Inextensional Deformation of Cantilevered Plates

1979 ◽  
Vol 46 (3) ◽  
pp. 631-636 ◽  
Author(s):  
J. G. Simmonds ◽  
A. Libai
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Conditions ◽  
Independent Set ◽  
Straight Edge ◽  
The Other ◽  
Subsequent Paper ◽  
First Order ◽  
Alternate Forms ◽  
Approximate Equations

A set of first-order ordinary differential equations with initial conditions is derived for the exact, nonlinear, inextensional deformation of a loaded plate bounded by two straight edges and two curved ones. The analysis extends earlier approximate work of Mansfield and Kleeman, Ashwell, and Lin, Lin, and Mazelsky. For a plate clamped along one straight edge and subject to a force and couple along the other, there are 13 differential equations, but an independent set of 9 may be split off. In a subsequent paper, we consider alternate forms of these 9 equations for plates that twist as they deform. Their structure and solutions are compared to Mansfield’s approximate equations and particular attention is given to tip-loaded triangular plates.

The Strong Perfect Graph Conjecture for Planar Graphs

1973 ◽  
Vol 25 (1) ◽  
pp. 103-114 ◽  
Author(s):  
Alan Tucker
Keyword(s):  
Chromatic Number ◽  
Planar Graphs ◽  
Independent Set ◽  
Independent Sets ◽  
Clique Number ◽  
Perfect Graph ◽  
Stability Number ◽  
Partition Number ◽  
Minimum Number ◽  
The Stability

A graph G is called γ-perfect if ƛ (H) = γ(H) for every vertex-generated subgraph H of G. Here, ƛ(H) is the clique number of H (the size of the largest clique of H) and γ(H) is the chromatic number of H (the minimum number of independent sets of vertices that cover all vertices of H). A graph G is called α-perfect if α(H) = θ(H) for every vertex-generated subgraph H of G, where α (H) is the stability number of H (the size of the largest independent set of H) and θ(H) is the partition number of H (the minimum number of cliques that cover all vertices of H).

New Metrics for Evaluating Whiteness of Fluorescent Samples

2019 ◽  
Vol 2019 (1) ◽  
pp. 247-251
Author(s):  
Lv X. ◽  
Wang Y.Z. ◽  
M. Wei ◽  
Luo M.R.
Keyword(s):  
Magnitude Estimation ◽  
Independent Set ◽  
Accurate Prediction ◽  
The Other ◽  
Appearance Model ◽  
Low Level ◽  
Adaptation Factor ◽  
Colour Appearance

A magnitude estimation experiment was carried out to scale the extent of whiteness from a set of near white textile samples including fluorescent white agent. Each was assessed under 4 different CCTs, each having a high and a low level of UV energy. The results were used to test various existing whiteness formulae. Finally, by fitting to the present data, two new metrics were developed. One is based on CIECAM02, and the other is based on the present CIE whiteness formula by transforming the data to D65 chromaticity from the other white sources via CAT02 chromatic adaption transform with a proper incomplete adaptation factor (D). It was also tested using an independent set of data. Both formulae gave accurate prediction to the data. The former metric is proposed because it is based on a colour appearance model.

scholarly journals Evaluating Plastic Deformation and Damage as Potential Mechanisms for Tendon Inelasticity Using a Reactive Modeling Framework

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Babak N. Safa ◽  
Andrea H. Lee ◽  
Michael H. Santare ◽  
Dawn M. Elliott
Keyword(s):  
Plastic Deformation ◽  
Mechanical Response ◽  
Independent Set ◽  
Tensile Tests ◽  
The Other ◽  
Modeling Framework ◽  
Validation Data ◽  
Molecular Bond ◽  
Bond Kinetics ◽  
Comprehensive Framework

Inelastic behaviors, such as softening, a progressive decrease in modulus before failure, occur in tendon and are important aspects in degeneration and tendinopathy. These inelastic behaviors are generally attributed to two potential mechanisms: plastic deformation and damage. However, it is not clear which is primarily responsible. In this study, we evaluated these potential mechanisms of tendon inelasticity by using a recently developed reactive inelasticity model (RIE), which is a structurally inspired continuum mechanics framework that models tissue inelasticity based on the molecular bond kinetics. Using RIE, we formulated two material models, one specific to plastic deformation and the other to damage. The models were independently fit to published macroscale experimental tensile tests of rat tail tendons. We quantified the inelastic effects and compared the performance of the two models in fitting the mechanical response during loading, relaxation, unloading, and reloading phases. Additionally, we validated the models by using the resulting fit parameters to predict an independent set of experimental stress–strain curves from ramp-to-failure tests. Overall, the models were both successful in fitting the experiments and predicting the validation data. However, the results did not strongly favor one mechanism over the other. As a result, to distinguish between plastic deformation and damage, different experimental protocols will be needed. Nevertheless, these findings suggest the potential of RIE as a comprehensive framework for studying tendon inelastic behaviors.

scholarly journals Relaxed Two-Coloring of Cubic Graphs

2005 ◽  
Vol DMTCS Proceedings vol. AE,... (Proceedings) ◽  
Author(s):  
Robert Berke ◽  
Tibor Szabó
Keyword(s):  
Regular Graph ◽  
Maximum Degree ◽  
Independent Set ◽  
The Other ◽  
Cubic Graphs ◽  
Other Hand ◽  
Color Class ◽  
International Audience

International audience We show that any graph of maximum degree at most $3$ has a two-coloring, such that one color-class is an independent set while the other color induces monochromatic components of order at most $189$. On the other hand for any constant $C$ we exhibit a $4$-regular graph, such that the deletion of any independent set leaves at least one component of order greater than $C$. Similar results are obtained for coloring graphs of given maximum degree with $k+ \ell$ colors such that $k$ parts form an independent set and $\ell$ parts span components of order bounded by a constant. A lot of interesting questions remain open.

Alternate Exact Equations for the Inextensional Deformation of Arbitrary, Quadrilateral, and Triangular Plates

1979 ◽  
Vol 46 (4) ◽  
pp. 895-900 ◽  
Author(s):  
J. G. Simmonds ◽  
A. Libai
Keyword(s):  
Differential Equations ◽  
Independent Set ◽  
Straight Edge ◽  
The Other ◽  
Dimensionless Form ◽  
Numerical Example ◽  
Quadrilateral Plate

Previously, a set of 9 exact differential equations was derived for the inextensional deformation of a plate bounded by two straight edges and two arbitrary curves. One straight edge is built-in. The other moves rigidly and is subject to a force and couple. The curved edges are stress-free. If the plate twists as it deforms, then, as shown herein, the 9 equations may be replaced by 7. The equations are written in a dimensionless form allowing a ready comparison with Mansfield’s theory that assumes small but finite angles of rotation. If the end load is a couple only, then an independent set of 5 equations emerges. These reduce to 4 for a quadrilateral plate. A numerical example compares the prediction of the exact equations against those of Mansfield. For triangular plates under tip forces only, an alternate, better conditioned, set of 9 differential equations is derived, and the behavior of the solutions near the tip is analyzed.

scholarly journals Comparative analysis of principal components can be misleading

2014 ◽  
Author(s):  
Josef C Uyeda ◽  
Daniel S. Caetano ◽  
Matthew W Pennell
Keyword(s):  
Comparative Analysis ◽  
Quantitative Genetics ◽  
Principal Components ◽  
Independent Set ◽  
The State ◽  
Comparative Data ◽  
The Other ◽  
Phenotypic Trait ◽  
Correlated Evolution ◽  
Evolutionary Response

Quantitative geneticists long ago recognized the value of studying evolution in a multivariate framework (Pearson, 1903). Due to linkage, pleiotropy, coordinated selection and mutational covariance, the evolutionary response in any phenotypic trait can only be properly understood in the context of other traits (Lande, 1979; Lynch and Walsh, 1998). This is of course also well-appreciated by comparative biologists. However, unlike in quantitative genetics, most of the statistical and conceptual tools for analyzing phylogenetic comparative data (recently reviewed in Pennell and Harmon, 2013) are designed for analyzing a single trait (but see, for example Revell and Harmon, 2008; Revell and Harrison, 2008; Hohenlohe and Arnold, 2008; Revell and Collar, 2009; Schmitz and Motani, 2011; Adams, 2014b). Indeed, even classical approaches for testing for correlated evolution between two traits (e.g., Felsenstein, 1985; Grafen, 1989; Harvey and Pagel, 1991) are not actually multivariate as each trait is assumed to have evolved under a process that is independent of the state of the other (Hansen and Orzack, 2005; Hansen and Bartoszek, 2012). As a result of these limitations, researchers with multivariate datasets are often faced with a choice: analyze each trait as if they were independent or else decompose the dataset into statistically independent set of traits, such that each set can be analyzed with the univariate methods.

scholarly journals Minimum Partition of an r − Independence System

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Zill-e-Shams ◽  
Muhammad Salman ◽  
Zafar Ullah ◽  
Usman Ali
Keyword(s):  
Graph Partitioning ◽  
Applied Mathematics ◽  
Independent Set ◽  
Maximal Independent Set ◽  
Metric Dimension ◽  
Partition Problem ◽  
Maximum Cardinality ◽  
Minimal Set ◽  
Independence System ◽  
Wheel Graphs

Graph partitioning has been studied in the discipline between computer science and applied mathematics. It is a technique to distribute the whole graph data as a disjoint subset to a different device. The minimum graph partition problem with respect to an independence system of a graph has been studied in this paper. The considered independence system consists of one of the independent sets defined by Boutin. We solve the minimum partition problem in path graphs, cycle graphs, and wheel graphs. We supply a relation of twin vertices of a graph with its independence system. We see that a maximal independent set is not always a minimal set in some situations. We also provide realizations about the maximum cardinality of a minimum partition of the independence system. Furthermore, we study the comparison of the metric dimension problem of a graph with the minimum partition problem of that graph.

scholarly journals An efficient connected dominating set algorithm in WSNs based on the induced tree of the crossed cube

2015 ◽  
Vol 25 (2) ◽  
pp. 295-309 ◽  
Author(s):  
Jing Zhang ◽  
Shu-Ming Zhou ◽  
Li Xu ◽  
Wei Wu ◽  
Xiucai Ye
Keyword(s):  
Dominating Set ◽  
Fibonacci Sequence ◽  
Independent Set ◽  
Connected Dominating Set ◽  
Maximal Independent Set ◽  
Virtual Backbone ◽  
Np Hard Problem ◽  
Save Energy ◽  
Crossed Cube ◽  
Interference Problems

Abstract The connected dominating set (CDS) has become a well-known approach for constructing a virtual backbone in wireless sensor networks. Then traffic can forwarded by the virtual backbone and other nodes turn off their radios to save energy. Furthermore, a smaller CDS incurs fewer interference problems. However, constructing a minimum CDS is an NP-hard problem, and thus most researchers concentrate on how to derive approximate algorithms. In this paper, a novel algorithm based on the induced tree of the crossed cube (ITCC) is presented. The ITCC is to find a maximal independent set (MIS), which is based on building an induced tree of the crossed cube network, and then to connect the MIS nodes to form a CDS. The priority of an induced tree is determined according to a new parameter, the degree of the node in the square of a graph. This paper presents the proof that the ITCC generates a CDS with a lower approximation ratio. Furthermore, it is proved that the cardinality of the induced trees is a Fibonacci sequence, and an upper bound to the number of the dominating set is established. The simulations show that the algorithm provides the smallest CDS size compared with some other traditional algorithms.

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