Symmetric Graphs Research Articles

CFD Simulation and Experiments of Pneumatic Centralized Cylinder Metering Device Cavity and Airflow Distributor

The distribution of airflow field in the pneumatic centralized cylinder metering device cavity, airstream distributor and different angle seed feeding tubes was investigated based on the pneumatic centralized cylinder direct-seeding metering device to study the effect on the movement law of rice seed. In total, three suction hole sizes (1.5 mm, 2 mm and 2.0 mm 45° wedge) were used for CFD simulation. The results showed that under the same inlet vacuum, the pressure at the 1.5 mm hole is higher than the other two types of holes, and the five measurement points of the 2 mm hole are more stable than the other two types of holes. At the positive pressure seed feeding area, the inlet pressure was set as 1.5 kPa, and the outlet pressure was set as 0 Pa. The pressure distribution at different measuring points showed that the 2 mm 45° wedge had the most uneven positive pressure distribution, and the 1.5 mm hole had higher positive pressure distribution than the 2 mm hole in general. Three different structured airflow distributors were designed. CFD simulation experiments showed that the arc transition type presented better uniformity than the other two types. The uniformity experiments at the ends of the seed-feeding tubes indicated that the airflow velocity had the trend of large in the middle and small at two sides. Finally, the movement law of the rice seeds in seed feeding tubes at different angles was obtained by using high-speed photography. The results showed that the rice seeds in tube C (maximum angle) presented a movement posture of falling sector a and kept falling after colliding in sector b; the rice seeds in tube B (the second angle) presented a movement posture of falling in sector a and kept falling after colliding in sector b. The above research provides a reference for the optimal design of a pneumatic centralized cylinder metering device.

On p-competition graphs of loopless Hamiltonian digraphs without symmetric arcs and graph operations

For a digraph $D$, the $p$-competition graph $C_{p}(D)$ of $D$ is the graph satisfying the following: $V(C_{p}(D))=V(D)$, for $x,y \in V(C_{p}(D))$, $xy \in E(C_{p}(D))$ if and only if there exist distinct $p$ vertices $v_{1},$ $v_{2},$ $...,$ $v_{p}$ $\in$ $V(D)$ such that $x \rightarrow v_{i}$, $y \rightarrow v_{i}$ $\in$ $A(D)$ for each $i=1,2,$ $...,$ $p$. We show the $H_1 \cup H_2$ is a $p$-competition graph of a loopless digraph without symmetric arcs for $p \geq 2$, where $H_1$ and $H_2$ are $p$-competition graphs of loopless digraphs without symmetric arcs and $V(H_1) \cap V(H_2)$ $=$ $\{ \alpha \}$. For $p$-competition graphs of loopless Hamiltonian digraphs without symmetric arcs, we obtain similar results. And we show that a star $K_{1,n}$ is a $p$-competition graph of a loopless Hamiltonian digraph without symmetric arcs if $n \geq 2p+3$ and $p \geq 3$. Based on these results, we obtain conditions such that spiders, caterpillars and cacti are $p$-competition graphs of loopless digraphs without symmetric arcs. We also obtain conditions such that these graphs are $p$-competition graphs of loopless Hamiltonian digraphs without symmetric arcs.

Arc-transitive trivalent Cayley graphs

A combinatorial graph Γ is symmetric, or arc-transitive, if its automorphism group acts transitively on the arcs of Γ, and s-arc-transitive (resp. s-arc-regular) if its automorphism group acts transitively (resp. regularly) on the set of s-arcs of Γ, which are the walks of length s in Γ in which any three consecutive vertices are distinct. It was shown by Tutte (1947, 1959) that every finite symmetric trivalent graph is s-arc-regular for some s≤5. Djoković and Miller (1980) took this further by showing that there are seven types of arc-transitive group action on finite trivalent graphs, characterised by the stabilisers of a vertex and an edge. The latter classification was refined by Conder and Nedela (2009), in terms of what types of arc-transitive subgroup can occur in the automorphism group of Γ.In this paper we address the question of when a finite trivalent Cayley graph is arc-transitive, by determining when a connected finite arc-transitive trivalent graph is a Cayley graph. We show that in five of the 17 Conder-Nedela classes, there is no Cayley graph, while in two others, every graph is a Cayley graph. In eight of the remaining ten classes, we give necessary conditions on the order of the graph for it to be Cayley; there is no such condition in the other two. Also we show that in each of those last ten classes, there are infinitely many Cayley graphs and infinitely many non-Cayley graphs.

On 7-valent symmetric Cayley graphs of finite simple groups

On 7-valent symmetric Cayley graphs of finite simple groups

Design of Neural Network Model for Cross-Media Audio and Video Score Recognition Based on Convolutional Neural Network Model.

In this paper, the residual convolutional neural network is used to extract the note features in the music score image to solve the problem of model degradation; then, multiscale feature fusion is used to fuse the feature information of different levels in the same feature map to enhance the feature representation ability of the model. A network composed of a bidirectional simple loop unit and a chained time series classification function is used to identify notes, parallelizing a large number of calculations, thereby speeding up the convergence speed of training, which also makes the data in the dataset no longer need to be strict with labels. Alignment also reduces the requirements on the dataset. Aiming at the problem that the existing cross-modal retrieval methods based on common subspace are insufficient for mining local consistency within modalities, a cross-modal retrieval method fused with graph convolution is proposed. The K-nearest neighbor algorithm is used to construct modal graphs for samples of different modalities, and the original features of samples from different modalities are encoded through a symmetric graph convolutional coding network and a symmetric multilayer fully connected coding network, and the encoded features are fused and input. We jointly optimize the intramodal semantic constraints and intermodal modality-invariant constraints in the common subspace to learn highly locally consistent and semantically consistent common representations for samples from different modalities. The error value of the experimental results is used to illustrate the effect of parameters such as the number of iterations and the number of neurons on the network. In order to more accurately illustrate that the generated music sequence is very similar to the original music sequence, the generated music sequence is also framed, and finally the music sequence spectrogram and spectrogram are generated. The accuracy of the experiment is illustrated by comparing the spectrogram and the spectrogram, and genre classification predictions are also performed on the generated music to show that the network can generate music of different genres.

Locality preserving projection with symmetric graph embedding for unsupervised dimensionality reduction

Preserving the intrinsic structure of data is very important for unsupervised dimensionality reduction. For structure preserving, graph embedding technique is widely considered. However, most of the existing unsupervised graph embedding based methods cannot effectively preserve the intrinsic structure of data since these methods either use the constant graph or only explore the geometric structure based on the distance information or representation information. To solve this problem, a novel method, called locality preserving projection with symmetric graph embedding (LPP_SGE), is proposed. LPP_SGE introduces a novel adaptive graph learning model and can obtain the intrinsic graph and projection in a unified framework by fully exploring the representation information and distance information of the original data. Different from the existing works which generally introduce no less than two constraints to capture the representation information and distance information, LPP_SGE can simultaneously capture the above two kinds of structure information in one term. Moreover, LPP_SGE introduces an ‘l2,1’ norm based projection constraint to select the most discriminative features from the complex data for dimensionality reduction, such that the robustness is enhanced. Experimental results on four databases and two kinds of noisy databases show that LPP_SGE performs better than many well-known methods.

Star Chromatic Index of 1-Planar Graphs

Many symmetric properties are well-explored in graph theory, especially in graph coloring, such as symmetric graphs defined by the automorphism groups, symmetric drawing of planar graphs, and symmetric functions which are used to count the number of specific colorings of a graph. This paper is devoted to studying the star edge coloring of 1-planar graphs. The star chromatic index χst′(G) of a graph G is defined as the smallest k for which the edges of G can be colored by using k colors so that no two adjacent edges get the same color and no bichromatic paths or cycles of length four are produced. A graph G is called 1-planar if it can be drawn in the plane such that each edge crosses at most one other edge. In this paper, we prove that every 1-planar graph G satisfies χst′(G)≤7.75Δ+166; and moreover χst′(G)≤⌊1.5Δ⌋+500 if G contains no 4-cycles, and χst′(G)≤2.75Δ+116 if G is 3-connected, or optimal, or NIC-planar.

On the Generalized $\vartheta$-Number and Related Problems for Highly Symmetric Graphs

This paper is an in-depth analysis of the generalized $\vartheta$-number of a graph. The generalized $\vartheta$-number, $\vartheta_k(G)$, serves as a bound for both the $k$-multichromatic number of a graph and the maximum $k$-colorable subgraph problem. We present various properties of $\vartheta_k(G)$, such as that the sequence $(\vartheta_k(G))_k$ is increasing and bounded from above by the order of the graph $G$. We study $\vartheta_k(G)$ when $G$ is the strong, disjunction, or Cartesian product of two graphs. We provide closed form expressions for the generalized $\vartheta$-number on several classes of graphs including the Kneser graphs, cycle graphs, strongly regular graphs, and orthogonality graphs. Our paper provides bounds on the product and sum of the $k$-multichromatic number of a graph and its complement graph, as well as lower bounds for the $k$-multichromatic number on several graph classes including the Hamming and Johnson graphs.

Classification of Arc-Transitive Elementary Abelian Covers of the C13 Graph

Let Γ be a graph and G⩽Aut(Γ). A graph Γ can be called G-arc-transitive (GAT) if G acts transitively on its arc set. A regular covering projection p:Γ¯→Γ is arc-transitive (AT) if an AT subgroup of Aut(Γ) lifts under p. In this study, by applying a number of concepts in linear algebra such as invariant subspaces (IVs) of matrix groups (MGs), we discuss regular AT elementary abelian covers (R-AT-EA-covers) of the C13 graph.

A New Accelerated Fixed-Point Algorithm for Classification and Convex Minimization Problems in Hilbert Spaces with Directed Graphs

A new accelerated algorithm for approximating the common fixed points of a countable family of G-nonexpansive mappings is proposed, and the weak convergence theorem based on our main results is established in the setting of Hilbert spaces with a symmetric directed graph G. As an application, we apply our results for solving classification and convex minimization problems. We also apply our proposed algorithm to estimate the weight connecting the hidden layer and output layer in a regularized extreme learning machine. For numerical experiments, the proposed algorithm gives a higher performance of accuracy of the testing set than that of FISTA-S, FISTA, and nAGA.

Symmetries in graphs via simplicial automorphisms

An automorphism ρ of a graph X is said to be semiregular provided all of its cycles in its cycle decomposition are of the same length, and is said to be simplicial if it is semiregular and the quotient multigraph Xρ of X with respect to ρ is a simple graph, and thus of the same valency as X. It is shown that, with the exception of the complete graph K4, the Petersen graph, the Coxeter graph and the so called H-graph (alternatively denoted as S(17), the smallest graph in the family of the so called Sextet graphs S(p), p≡±1(mod16)), every cubic arc-transitive graph with a primitive automorphism group admits a simplicial automorphism.

2-Arc-transitive hexavalent Cayley graphs on nonabelian simple groups

A plenty of contributions have been done on symmetric Cayley graphs on nonabelian simple groups, but the only known complete classification of such graphs with composite valency is of valency 4 (provided 2-arc-transitivity) by Fang et al. [Europ. J. Combin. 25 (2004), 1107–1116] and Du and Feng [Comm. Algebra 47 (2019), 4565–4574]. This naturally motivates this work for classifying 2-arc-transitive hexavalent Cayley graphs on nonabelian simple groups. It is proved that these graphs are either normal or -arc-transitive Cayley graphs on where n is among 11 specific numbers dividing A specific example is also constructed.

An explicit characterization of cubic symmetric bi-Cayley graphs on nonabelian simple groups

One of the remarkable contributions in the study of symmetric Cayley graphs on nonabelian simple groups is the complete classification of such graphs that are cubic and nonnormal. This naturally motivates the study of cubic (normal and nonnormal) symmetric bi-Cayley graphs on nonabelian simple groups. In this paper, the full automorphism groups of these graphs are determined, and necessary and sufficient conditions are given for a graph being a cubic normal symmetric Cayley or bi-Cayley graph on a nonabelian simple group (one may then find many examples). As an application, we also prove that cubic symmetric Cayley graphs on nonabelian simple groups are stable.

Focal Mechanism Analysis of the Earthquakes Beneath the Sunda-Banda Arc Transition, Indonesia, Using the BMKG Data

Structural complexity in the Sunda-Banda arc transition is a topic of much debate amongst Earth scientists. We have processed focal mechanism study using moment tensor inversion for 20 events in the region using the Agency for Meteorology, Climatology, and Geophysics (BMKG) data from 2014-2016 for earthquakes of magnitude Mw ≥ 5.0. Our result shows different solutions that depend on the source region of the earthquakes that include subduction zones and collision zones, which host active faults and the back-arc thrusts. Earthquakes that occurred in the subduction zone appear to rupture on thrust faults for shallow and intermediate events, while the deep events have normal fault mechanisms. The shallow events in the collision zone occur on thrust faults with differing strike directions, but generally, there are largely parallel to the Timor trough. We also found normal fault mechanisms at play for deep events below the collision zone. The occurrence of deep earthquakes in this area is consistent with remnant slab activity that persists to the present day. Focal mechanism solutions for shallow events in the north of Sumbawa island indicate a thrust fault with a strike direction that is almost parallel to the back-arc thrust in this area. We also found evidence of strike-slip motion along local-scale active faults in the area.

Optimization of Synchropulsed MIG Welding Process Parameters for Welding of AW 5083 Sheets

Metal inert gas (MIG) welding is one of the processes most commonly used for joining metals, especially for joining aluminum and its alloys. The application of a pulsed current in an electric arc allows better controllability of the molten droplets and the arc transition, which subsequently leads to welds with characteristic flaky joints of better quality. In this paper, the optimization of parameters for welding aluminum alloys using the synchropulse welding process is investigated. By observing the input variables that have the greatest influence on the change in appearance of the welding current characteristics (delta wire feed from 0.1 to 6.0 m/min, frequency F from 0.5 to 3 Hz, duty cycle from 10% to 90%), it is possible to perform an optimization to achieve the desired output values. The output variables of the experiments are defined as insufficient/excessive throat thickness (mm), depth of penetration (mm), and weld width (mm); and for the desired quality of the welded joint the most acceptable range of its values is selected, the numerical optimization implementation. The experiment has shown that the delta wire feed has the greatest effect on the observed properties, while the influence of frequency F and duty cycle is somewhat smaller, but the factors responsible for the observed output properties are still significant. From all this, it is possible to select specific values of these input variables to define the best possible observed properties and to determine the characteristics of the defined mathematical models.

Symmetric graph of a ring with involution

Symmetric graph of a ring with involution

Prime Cordial Labeling of Generalized Petersen Graph under Some Graph Operations

A graph is a connection of objects. These objects are often known as vertices or nodes and the connection or relation in these nodes are called arcs or edges. There are certain rules to allocate values to these vertices and edges. This allocation of values to vertices or edges is called graph labeling. Labeling is prime cordial if vertices have allocated values from 1 to the order of graph and edges have allocated values 0 or 1 on a certain pattern. That is, an edge has an allocated value of 0 if the incident vertices have a greatest common divisor (gcd) greater than 1. An edge has an allocated value of 1 if the incident vertices have a greatest common divisor equal to 1. The number of edges labeled with 0 or 1 are equal in numbers or, at most, have a difference of 1. In this paper, our aim is to investigate the prime cordial labeling of rotationally symmetric graphs obtained from a generalized Petersen graph P(n,k) under duplication operation, and we have proved that the resulting symmetric graphs are prime cordial. Moreover, we have also proved that when we glow a Petersen graph with some path graphs, then again, the resulting graph is a prime cordial graph.

Hyper power impulse magnetron – HyPIM – glow discharge

Glow discharges are known to be limited for running at high currents (< 0.1 A · cm−2). Magnetically enhanced plasmas could overcome this limitation, typically for the magnetron operated in pulsed mode during a few 100μs. Hence, the current density could be increased by two decades, but it still stays below 10 A · cm−2. Here we report on a long (∼1 ms) pulsed operation of magnetrons, while preserving the glow mode, for current densities exceeding at least 3 times the highest current density reported for high power pulsed magnetrons. Even if the density of energy surpasses 7 J · cm−2, no arc transition was observed. Three target materials have been successfully tested: carbon (C), molybdenum (Mo) and tungsten (W) in helium atmosphere, from 5 to 30 Pa. Two key parameters are required to reach the Hyper Power Impulse Magnetron (HyPIM) glow mode: i) the accurate control of the maximum voltage during the pulse and ii) the use of the pre-ionization. Operating conditions of HyPIM will be presented and compared to other discharges.

Pentavalent symmetric graphs of order $$8p^2$$

Pentavalent symmetric graphs of order $$8p^2$$

An Accelerated Fixed-Point Algorithm with an Inertial Technique for a Countable Family of G-Nonexpansive Mappings Applied to Image Recovery

Many authors have proposed fixed-point algorithms for obtaining a fixed point of G-nonexpansive mappings without using inertial techniques. To improve convergence behavior, some accelerated fixed-point methods have been introduced. The main aim of this paper is to use a coordinate affine structure to create an accelerated fixed-point algorithm with an inertial technique for a countable family of G-nonexpansive mappings in a Hilbert space with a symmetric directed graph G and prove the weak convergence theorem of the proposed algorithm. As an application, we apply our proposed algorithm to solve image restoration and convex minimization problems. The numerical experiments show that our algorithm is more efficient than FBA, FISTA, Ishikawa iteration, S-iteration, Noor iteration and SP-iteration.