scholarly journals On Independent Secondary Dominating Sets in Generalized Graph Products

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2399
Author(s):  
Adrian Michalski ◽  
Paweł Bednarz
Keyword(s):  
Complete Characterization ◽  
Asymmetric Structure ◽  
Graph Products ◽  
Dominating Sets ◽  
Complete Problem ◽  
Join Of Graphs ◽  
Np Complete ◽  
Graph Parameters ◽  
Domination In Graphs

In 2008, Hedetniemi et al. introduced (1,k)-domination in graphs. The research on this concept was extended to the problem of existence of independent (1,k)-dominating sets, which is an NP-complete problem. In this paper, we consider independent (1,1)- and (1,2)-dominating sets, which we name as (1,1)-kernels and (1,2)-kernels, respectively. We obtain a complete characterization of generalized corona of graphs and G-join of graphs, which have such kernels. Moreover, we determine some graph parameters related to these sets, such as the number and the cardinality. In general, graph products considered in this paper have an asymmetric structure, contrary to other many well-known graph products (Cartesian, tensor, strong).

scholarly journals Computing the Interleaving Distance is NP-Hard

2019 ◽  
Vol 20 (5) ◽  
pp. 1237-1271 ◽  
Author(s):  
Håvard Bakke Bjerkevik ◽  
Magnus Bakke Botnan ◽  
Michael Kerber
Keyword(s):  
Computational Complexity ◽  
Complete Characterization ◽  
Np Hard ◽  
Slight Improvement ◽  
Approximation Factor ◽  
Distance Computation ◽  
Persistence Modules ◽  
Np Complete ◽  
Interleaving Distance

Abstract We show that computing the interleaving distance between two multi-graded persistence modules is NP-hard. More precisely, we show that deciding whether two modules are 1-interleaved is NP-complete, already for bigraded, interval decomposable modules. Our proof is based on previous work showing that a constrained matrix invertibility problem can be reduced to the interleaving distance computation of a special type of persistence modules. We show that this matrix invertibility problem is NP-complete. We also give a slight improvement in the above reduction, showing that also the approximation of the interleaving distance is NP-hard for any approximation factor smaller than 3. Additionally, we obtain corresponding hardness results for the case that the modules are indecomposable, and in the setting of one-sided stability. Furthermore, we show that checking for injections (resp. surjections) between persistence modules is NP-hard. In conjunction with earlier results from computational algebra this gives a complete characterization of the computational complexity of one-sided stability. Lastly, we show that it is in general NP-hard to approximate distances induced by noise systems within a factor of 2.

scholarly journals Graphs with Constant Sum of Domination and Inverse Domination Numbers

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
T. Tamizh Chelvam ◽  
T. Asir
Keyword(s):  
Minimum Degree ◽  
Dominating Set ◽  
Domination Number ◽  
Complete Characterization ◽  
Dominating Sets ◽  
Minimum Cardinality ◽  
Connected Graphs ◽  
Vertex Set ◽  
Domination Numbers

A subset D of the vertex set of a graph G, is a dominating set if every vertex in V−D is adjacent to at least one vertex in D. The domination number γ(G) is the minimum cardinality of a dominating set of G. A subset of V−D, which is also a dominating set of G is called an inverse dominating set of G with respect to D. The inverse domination number γ′(G) is the minimum cardinality of the inverse dominating sets. Domke et al. (2004) characterized connected graphs G with γ(G)+γ′(G)=n, where n is the number of vertices in G. It is the purpose of this paper to give a complete characterization of graphs G with minimum degree at least two and γ(G)+γ′(G)=n−1.

scholarly journals On the Laplacian spectra of product graphs

2015 ◽  
Vol 9 (1) ◽  
pp. 39-58 ◽  
Author(s):  
S. Barik ◽  
R.B. Bapat ◽  
S. Pati
Keyword(s):  
Cartesian Product ◽  
Complete Characterization ◽  
Graph Products ◽  
Lexicographic Product ◽  
Laplacian Spectrum ◽  
Strong Product ◽  
Laplacian Spectra ◽  
Product Graphs ◽  
Characteristic Sets

Graph products and their structural properties have been studied extensively by many researchers. We investigate the Laplacian eigenvalues and eigenvectors of the product graphs for the four standard products, namely, the Cartesian product, the direct product, the strong product and the lexicographic product. A complete characterization of Laplacian spectrum of the Cartesian product of two graphs has been done by Merris. We give an explicit complete characterization of the Laplacian spectrum of the lexicographic product of two graphs using the Laplacian spectra of the factors. For the other two products, we describe the complete spectrum of the product graphs in some particular cases. We supply some new results relating to the algebraic connectivity of the product graphs. We describe the characteristic sets for the Cartesian product and for the lexicographic product of two graphs. As an application we construct new classes of Laplacian integral graphs.

scholarly journals Optimal Bounds for the Change-Making Problem

1991 ◽  
Vol 20 (371) ◽  
Author(s):  
Dexter Kozen ◽  
Shmuel Zaks
Keyword(s):  
Greedy Algorithm ◽  
Related Problem ◽  
Complete Characterization ◽  
Fixed Number ◽  
Simple Test ◽  
Optimal Representation ◽  
Optimal Bounds ◽  
Np Complete ◽  
The Greedy Algorithm

<p>The change-making problem is the problem of representing a given value with the fewest coins possible. We investigate the problem of determining whether the greedy algorithm produces an optimal representation of all amounts for a given set of coin denominations 1 = c_1 &lt; c_2 &lt; ... &lt; c_m. Chang and Gill show that if the greedy algorithm is not always optimal, then there exists a counterexample x in the range</p><p>c_3 &lt;= x &lt; (c_m(c_m c_m-1 + c_m - 3c_m-1)) \ (c_m - c_m-1).</p><p>To test for the existence of such a counterexample, Chang and Gill propose computing and comparing the greedy and optimal representations of all x in this range. In this paper we show that if a counterexample exists, then the smallest one lies in the range c_3 + 1 &lt; x &lt; c_m + c_m-1, and these bounds are tight. Moreover, we give a simple test for the existence of a counterexample that does not require the calculation of optimal representations.</p><p>In addition, we give a complete characterization of three-coin systems and an efficient algorithm for all systems with a fixed number of coins. Finally, we show that a related problem is <em>co</em>NP-complete.</p>

ON UNIVERSALLY POLYNOMIAL CONTEXT-FREE LANGUAGES

2002 ◽  
Vol 13 (06) ◽  
pp. 829-835
Author(s):  
NICHOLAS TRAN
Keyword(s):  
Complete Characterization ◽  
Automatic Method ◽  
Intractable Problems ◽  
Np Complete ◽  
Open Question ◽  
Context Free

A language is universally polynomial if its intersection with every NP-complete language is in P. Such a language would provide an automatic method for generating easy instances of intractable problems. In this note, we give a complete characterization of universally polynomial languages that are context-free, answering an open question in [4].

On the Graph Parameters of Special Networks

2014 ◽  
Vol 543-547 ◽  
pp. 2977-2980
Author(s):  
Jian Xiang Cao ◽  
Xin Feng ◽  
Zheng Tao Jiang
Keyword(s):  
Communication Networks ◽  
Interconnection Network ◽  
Domination Number ◽  
Algorithm Design ◽  
The Sun ◽  
Dominating Sets ◽  
Link Failures ◽  
Bondage Number ◽  
Graph Parameters ◽  
Domination In Graphs

Domination in graphs has become one of the major areas of graph theory with extensive applications in design and analysis of communication networks, computational complexity, and algorithm design. This paper mainly research on domination number and bondage number of the graph, especially, these parameters measure to some extent the robustness of an interconnection network with respect to link failures. By constructing a family of minimum dominating sets we compute the domination number and bondage number of the sun graph.

A Complete Characterization of the Path Layout Construction Problem for ATM Networks with Given Hop Count and Load

1998 ◽  
Vol 08 (02) ◽  
pp. 207-220 ◽  
Author(s):  
Tamar Eilam ◽  
Michele Flammini ◽  
Shmuel Zaks
Keyword(s):  
Time Complexity ◽  
High Speed ◽  
Complete Characterization ◽  
Atm Networks ◽  
Hop Count ◽  
Construction Problem ◽  
Stretch Factor ◽  
Virtual Paths ◽  
Np Complete

We investigate the time complexity of deciding the existence of layouts of virtual paths in high-speed networks, that enable a connection from one vertex to all others and have maximum hop count h and maximum edge load l, for a stretch factor of one. We prove that the problem of determining the existence of such layouts is NP-complete for every given values of h and l, except for the cases h = 2, l = 1 and h = 1, any l, for which we give polynomial-time layout constructions. Extensions for cases of a stretch factor greater than one are also discussed.

Experimental Characterization of Mechanical Behavior of Cord-Rubber Composites

1982 ◽  
Vol 10 (1) ◽  
pp. 37-54 ◽  
Author(s):  
M. Kumar ◽  
C. W. Bert
Keyword(s):  
Response Characteristic ◽  
Cord Compression ◽  
Complete Characterization ◽  
Strain Response ◽  
Strain Gages ◽  
Experimental Characterization ◽  
Rubber Composites ◽  
Stress Strain ◽  
Strain Data

Abstract Unidirectional cord-rubber specimens in the form of tensile coupons and sandwich beams were used. Using specimens with the cords oriented at 0°, 45°, and 90° to the loading direction and appropriate data reduction, we were able to obtain complete characterization for the in-plane stress-strain response of single-ply, unidirectional cord-rubber composites. All strains were measured by means of liquid mercury strain gages, for which the nonlinear strain response characteristic was obtained by calibration. Stress-strain data were obtained for the cases of both cord tension and cord compression. Materials investigated were aramid-rubber, polyester-rubber, and steel-rubber.

Characterization of CMOS Structures (0.6 µm process) Submitted to HBM and COM ESD Stress Tests

1997 ◽  
Author(s):  
G. Meneghesso ◽  
E. Zanoni ◽  
P. Colombo ◽  
M. Brambilla ◽  
R. Annunziata ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Electrostatic Discharge ◽  
Stress Test ◽  
Complete Characterization ◽  
Stress Tests ◽  
Test Procedures ◽  
Emission Microscopy ◽  
Fast Rise ◽  
Scanning Electron

Abstract In this work, we present new results concerning electrostatic discharge (ESD) robustness of 0.6 μm CMOS structures. Devices have been tested according to both HBM and socketed CDM (sCDM) ESD test procedures. Test structures have been submitted to a complete characterization consisting in: 1) measurement of the tum-on time of the protection structures submitted to pulses with very fast rise times; 2) ESD stress test with the HBM and sCDM models; 3) failure analysis based on emission microscopy (EMMI) and Scanning Electron Microscopy (SEM).

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