scholarly journals Structure of Cubic Lehman Matrices

10.37236/7947 ◽  
2019 ◽  
Vol 26 (3) ◽  
Author(s):  
Dillon Mayhew ◽  
Irene Pivotto ◽  
Gordon Royle
Keyword(s):  
Bipartite Graph ◽  
Adjacency Matrix ◽  
Computational Study ◽  
Computational Results ◽  
Alpha Omega ◽  
Regular Bipartite Graph

A pair $(A,B)$ of square $(0,1)$-matrices is called a Lehman pair if $AB^T=J+kI$ for some integer $k\in\{-1,1,2,3,\ldots\}$. In this case $A$ and $B$ are called Lehman matrices. This terminology arises because Lehman showed that the rows with the fewest ones in any non-degenerate minimally nonideal (mni) matrix $M$ form a square Lehman submatrix of $M$. Lehman matrices with $k=-1$ are essentially equivalent to partitionable graphs (also known as $(\alpha,\omega)$-graphs), so have been heavily studied as part of attempts to directly classify minimal imperfect graphs. In this paper, we view a Lehman matrix as the bipartite adjacency matrix of a regular bipartite graph, focusing in particular on the case where the graph is cubic. From this perspective, we identify two constructions that generate cubic Lehman graphs from smaller Lehman graphs. The most prolific of these constructions involves repeatedly replacing suitable pairs of edges with a particular $6$-vertex subgraph that we call a $3$-rung ladder segment. Two decades ago, Lütolf & Margot initiated a computational study of mni matrices and constructed a catalogue containing (among other things) a listing of all cubic Lehman matrices with $k =1$ of order up to $17 \times 17$.  We verify their catalogue (which has just one omission), and extend the computational results to $20 \times 20$ matrices. Of the $908$ cubic Lehman matrices (with $k=1$) of order up to $20 \times 20$, only two do not arise from our $3$-rung ladder construction. However these exceptions can be derived from our second construction, and so our two constructions cover all known cubic Lehman matrices with $k=1$.

scholarly journals Normalized Sombor Indices as Complexity Measures of Random Networks

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 976
Author(s):  
R. Aguilar-Sánchez ◽  
J. Méndez-Bermúdez ◽  
José Rodríguez ◽  
José Sigarreta
Keyword(s):  
Random Matrix ◽  
Adjacency Matrix ◽  
Matrix Theory ◽  
Computational Study ◽  
Random Networks ◽  
Geometric Graphs ◽  
Theory Approach ◽  
Complexity Measures ◽  
Random Geometric Graphs ◽  
Highly Correlated

We perform a detailed computational study of the recently introduced Sombor indices on random networks. Specifically, we apply Sombor indices on three models of random networks: Erdös-Rényi networks, random geometric graphs, and bipartite random networks. Within a statistical random matrix theory approach, we show that the average values of Sombor indices, normalized to the order of the network, scale with the average degree. Moreover, we discuss the application of average Sombor indices as complexity measures of random networks and, as a consequence, we show that selected normalized Sombor indices are highly correlated with the Shannon entropy of the eigenvectors of the adjacency matrix.

Computational Study of a Path-Based Algorithm and Its Variants for Static Traffic Assignment

1996 ◽  
Vol 1537 (1) ◽  
pp. 106-115 ◽  
Author(s):  
Carlos Sun ◽  
R. Jayakrishnan ◽  
Wei K. Tsai
Keyword(s):  
Line Search ◽  
Computational Study ◽  
Urban Traffic ◽  
Computer Memory ◽  
Traffic Networks ◽  
Computational Results ◽  
First Derivative ◽  
Line Search Techniques ◽  
Real Time Applications

Recent research has indicated that advances in computer memory have made the use of path-based algorithms in urban traffic networks a possibility. The path-based gradient projection (GP) offers significant benefits in computation times over the conventional Frank-Wolfe algorithm and may be especially suited for real-time applications. The computational results from applying GP to networks of up to 4,900 nodes, as well as the performance of different variants of GP, are discussed. Also discussed is the sensitivity of the results to parameters such as the number of destinations and the level of congestion. The variants of the basic GP algorithm examined are intended to further improve the per-iteration performance of the algorithm for larger networks. These variants include a GP version with a modified first derivative update and different versions that use line-search techniques, including a boundary stopping method. The results establish that GP indicates substantial benefits even for larger networks. The modifications, while they do improve the computation times per GP iteration, affect the convergence quality of the algorithm, indicating that the earlier GP algorithm is a better alternative for both large and small networks.

scholarly journals Spectral Extrema for Graphs: The Zarankiewicz Problem

10.37236/212 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
László Babai ◽  
Barry Guiduli
Keyword(s):  
Bipartite Graph ◽  
Spectral Radius ◽  
Upper Bound ◽  
Adjacency Matrix ◽  
Complete Bipartite Graph ◽  
Average Degree ◽  
Largest Eigenvalue ◽  
Zarankiewicz Problem ◽  
The Largest Eigenvalue

Let $G$ be a graph on $n$ vertices with spectral radius $\lambda$ (this is the largest eigenvalue of the adjacency matrix of $G$). We show that if $G$ does not contain the complete bipartite graph $K_{t ,s}$ as a subgraph, where $2\le t \le s$, then $$\lambda \le \Big((s-1)^{1/t }+o(1)\Big)n^{1-1/t }$$ for fixed $t$ and $s$ while $n\to\infty$. Asymptotically, this bound matches the Kővári-Turán-Sós upper bound on the average degree of $G$ (the Zarankiewicz problem).

Experimental and Computational Study of Effects of Viscosity of the Filter Media in a Developed Particulate Trapping System

2018 ◽  
Vol 9 (5) ◽  
Author(s):  
Y. Liu
Keyword(s):  
Experimental Data ◽  
Management System ◽  
Experimental Validation ◽  
Computational Study ◽  
Cost Effective ◽  
Manufacturing Cost ◽  
Present System ◽  
Computational Results ◽  
Experimental Assessment ◽  
Good Agreement

A cost effective, portable particulate management system was developed, prototyped, and evaluated for further application and commercialization, which could remove and dispose particulate matter suspended in air efficiently and safely. A prototype of the present system was built for experimental assessment and validation. The experimental data showed that the developed particulate management system can effectively clean the air by capturing the particles inside it. Effects of viscosity of filter medium on the performance of the developed system were also discussed. The present system is very flexible, whose size and shape can be scaled and changed to be fit for different applications. Its manufacturing cost is less than $10. Based on the experimental validation results, it was found that the present system can be further developed, commercialized, and applied for a variety of industries. The experiments and experimental data were simulated and validated using computer fluent dynamics. A relatively good agreement was achieved between the experimental and computational results.

A Computational Study of In-Cylinder NOx Reduction Strategies for a Compression-Ignition Engine Fueled With Diesel/Hydrogen Mixtures

2015 ◽  
Author(s):  
Hassan A. Khairallah ◽  
Umit O. Koylu
Keyword(s):  
Chemical Kinetics ◽  
Alternative Fuels ◽  
Computational Study ◽  
Nox Reduction ◽  
Nox Emissions ◽  
Computational Results ◽  
Detailed Chemical Kinetics ◽  
Compression Ignition Engine ◽  
Performance And Emission ◽  
Main Challenge

Considerable efforts have been made to introduce alternative fuels for use in conventional diesel and gasoline engines. There is significant interest in adding hydrogen to a diesel engine to reduce emissions and improve efficiency. However, the main challenge associated with the use of hydrogen in diesel engines is high nitrogen oxide (NOX) emissions. In the present study, a reduced chemical kinetics mechanism, consisting of 52 reactions and 29 chemical species for n-heptane fuel combustion, was incorporated with detailed chemical kinetics consisting of 29 reactions for hydrogen as well as additional nitrogen oxidation. This reaction mechanism was coupled with 3-D advanced CFD software to investigate the performance and emission characteristics of a diesel-hydrogen dual-fuel engine. Computational results showed good agreements with the experimental results for brake thermal efficiency, CO2, CO, and NOX emissions. The model was then employed to examine the effects of exhaust gas recirculation (EGR) and N2 dilution on NOX emissions. The computational results quantified the reduction in NOX emissions with EGR and N2 dilution, and a more remarkable reduction was found with 30% N2 dilution. However, in terms of the N2 dilution, a general decreasing trend was observed for both NOX and CO2 emissions, while CO emissions increased. In relation to the EGR, the NOX emissions decreased while CO2 and CO emissions significantly increased. Additionally, the results showed that the indicated mean effective pressure (IMEP) and indicated power decreased as the N2 dilution increased. The same trend was observed for the EGR but the reduction was less compared to that of the N2 dilution.

An Entropy Approach to the Hard-Core Model on Bipartite Graphs

2001 ◽  
Vol 10 (3) ◽  
pp. 219-237 ◽  
Author(s):  
JEFF KAHN
Keyword(s):  
Phase Transition ◽  
Bipartite Graph ◽  
Upper Bound ◽  
Hard Core ◽  
Independent Set ◽  
Independent Sets ◽  
Bipartite Graphs ◽  
Core Model ◽  
Hard Core Model ◽  
Regular Bipartite Graph

We use entropy ideas to study hard-core distributions on the independent sets of a finite, regular bipartite graph, specifically distributions according to which each independent set I is chosen with probability proportional to λ[mid ]I[mid ] for some fixed λ > 0. Among the results obtained are rather precise bounds on occupation probabilities; a ‘phase transition’ statement for Hamming cubes; and an exact upper bound on the number of independent sets in an n-regular bipartite graph on a given number of vertices.

scholarly journals C–O cleavage of aromatic oxygenates over ruthenium catalysts. A computational study of reactions at step sites

2015 ◽  
Vol 17 (23) ◽  
pp. 15324-15330 ◽  
Author(s):  
Cheng-chau Chiu ◽  
Alexander Genest ◽  
Armando Borgna ◽  
Notker Rösch
Keyword(s):  
Computational Study ◽  
Ruthenium Catalysts ◽  
Computational Results

C–O scissions of catecholate and phenolate on stepped Ru surfaces have accessible barriers. Computational results illustrate that benzene formation in the hydrodeoxygenation of aromatics over Ru occurs at step sites.

REGIOSELECTIVITY INVESTIGATION FOR THE PYROLYSIS OF XANTHATES: A COMPUTATIONAL STUDY

2013 ◽  
Vol 12 (07) ◽  
pp. 1350064 ◽  
Author(s):  
PING WU ◽  
JOHNNY TRUONG ◽  
YONGSHUN HUANG ◽  
JIAXING LI
Keyword(s):  
Oxygen Atom ◽  
Computational Study ◽  
Transition States ◽  
Major Product ◽  
Membered Ring ◽  
Computational Results ◽  
Atomic Size ◽  
Rate Determining Step ◽  
Ring Transition State ◽  
Step Mechanism

MP2/6-31+G(d,p)//MP2/6-31G(d) method was employed to investigate the pyrolyses of O -sec-butyl S -methyl xanthate (Chugeav reaction) and S -sec-butyl O -methyl xanthate, which gave regioselective products of E-butene, Z-butene and 1-butene. Both procedures were found to have 13 possible pathways, of which nine pathways would generate the alkene products. For O -sec-butyl S -methyl xanthate, the computational results indicated that the most favorable three pathways corresponded to a two-step mechanism, with the rate-determining step to be a thion sulfur atom involved six-membered ring transition states. The calculated products distribution was consistent with the experimental observations. However, for S -sec-butyl O -methyl xanthate, thiol-participated four-membered ring transition states were found to be more energetically favored than the six-membered ring transition state to produce 1-butene, which can be attributed to a larger sulfur atomic size than an oxygen atom. As the calculation result, only trace amount of 1-butene could be obtained with a major product being E-butene and Z-butene as a minority.

Design and off-design behavior of a tandem rotor stage

2019 ◽  
Vol 234 (4) ◽  
pp. 927-942 ◽  
Author(s):  
Amit Kumar ◽  
AM Pradeep
Keyword(s):  
Flow Separation ◽  
Computational Study ◽  
Adverse Pressure Gradient ◽  
Computational Results ◽  
Suction Surface ◽  
Compressor Blades ◽  
Tip Leakage ◽  
To Come ◽  
And Performance ◽  
Parametric Analyses

With an ever-increasing focus on clean and sustainable energy for transport and power, aero-engine designers need to come up with engine designs that can meet the efficiency and thrust requirements. In this aspect, compressor/fan designers always aim at designs that can result in higher pressure ratios and maximum possible efficiency with a fewer number of stages. Compressor blades, which are designed for higher diffusion, have an inherent risk of flow separation. This, therefore, fixes the upper permissible limit in terms of diffusion. If the suction surface adverse pressure gradient can be efficiently managed to avoid flow separation, it would be possible to target higher diffusion factors. One such concept for achieving this is using tandem blading. In the present computational study, a conventional low-speed compressor stage performance is compared with a tandem stage. Both designs attempt similar levels of targeted diffusion. The computational results are simulated at the design and the off-design conditions. The computational results are validated with experimental data. A high percentage pitch and low axial overlap configuration are finalized for the design of the tandem rotor based on existing literature as well as initial parametric analyses. The study shows that it is possible to achieve higher diffusion for the tandem rotor in comparison to a single rotor. The behavior of the gap-nozzle, interaction of the tip leakage with the gap-nozzle, blockage due to the tip leakage vortex, performance of stator, and performance of both stages are discussed in detail in this paper.

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