Academic literature on the topic 'Inner vertex number'

Let [Formula: see text] be a finite simple digraph with vertex set [Formula: see text]. A signed total Roman dominating function (STRDF) on a digraph [Formula: see text] is a function [Formula: see text] such that (i) [Formula: see text] for every [Formula: see text], where [Formula: see text] consists of all inner neighbors of [Formula: see text], and (ii) every vertex [Formula: see text] for which [Formula: see text] has an inner neighbor [Formula: see text] for which [Formula: see text]. The weight of an STRDF [Formula: see text] is [Formula: see text]. The signed total Roman domination number [Formula: see text] of [Formula: see text] is the minimum weight of an STRDF on [Formula: see text]. A set [Formula: see text] of distinct STRDFs on [Formula: see text] with the property that [Formula: see text] for each [Formula: see text] is called a signed total Roman dominating family (STRD family) (of functions) on [Formula: see text]. The maximum number of functions in an STRD family on [Formula: see text] is the signed total Roman domatic number of [Formula: see text], denoted by [Formula: see text]. In this paper, we initiate the study of signed total Roman domatic number in digraphs and we present some sharp bounds for [Formula: see text]. In addition, we determine the signed total Roman domatic number of some classes of digraphs.

We exhibit a connection between two constructions of twisted modules for a general vertex operator algebra with respect to inner automorphisms. We also study pseudo-derivations, pseudo-endomorphisms, and twist deformations of ordinary modules by pseudo-endomorphisms.

The difference of Zagreb indices of a graph G is defined as ΔM(G)=∑u∈V(G)(d(u))2−∑uv∈E(G)d(u)d(v), where d(x) denotes the degree of a vertex x in G. A Halin graph G is a graph that results from a plane tree T without vertices of degree two and with at least one vertex of degree at least three such that all leaves are joined through a cycle C in the embedded order. In this paper, we establish both lower and upper bounds on the difference of Zagreb indices for general Halin graphs and some special Halin graphs with fewer inner vertices. Furthermore, extremal graphs attaining related bounds are found.

We present an approach to compute the number of holes in binary images using the Vertex Chain Code (VCC); the VCC was developed for representing and analyzing 2D shapes composed of cells. Using this code, it is possible to relate the outer to inner vertices of any 2D shape and to find interesting properties. Now, in this paper, we describe more properties of the VCC, such as the computation of the connected regions in a hole, the analysis of complementary chains, the computation of the number of holes in a binary shape or image, the computation of the Euler number, and the detection of convex and concave shapes. Finally, in order to illustrate the capabilities of proposed methods, we present the computation of topological properties of examples of objects of the real world.

The tomato/potato psyllid Bactericera cockerelli (Sulc) (Hemiptera Triozidae) is found throughout most of New Zealand along with a range of native and other introduced psyllids all belonging to the superfamily Psylloidea The Psylloidea contains six families of which four are recorded from New Zealand (Psyllidae Calophyidae Homotomidae and Triozidae) Species belonging to Triozidae have trifurcate branching on the basal vein of the forewing in contrast to the other psyllid families in New Zealand which have bifurcate branching Bactericera cockerelli can be distinguished from other Triozidae species by the number of inner apical spurs on the tibiae of the hind legs (2) size and shape of the cubital cell in the forewing (short and compact) absence of long setae on vertex and dorsal thoracic surfaces and the lack of well developed genal cones Illustrations of these characters can be seen on insectwatchcom Usually body markings in insects are not suitable for identification purposes since these are likely to vary However the very distinct markings (white marginal and inner patch) on the vertex (dorsal surface of head) of B cockerelli seem stable and are a very useful characteristic for distinguishing this species from other psyllids in New Zealand

Let Λ denote a commutative ring with unity and D(Λ) denote a collection of all annihilating ideals from Λ. An annihilator intersection graph of Λ is represented by the notation AIG(Λ). This graph is not directed in nature, where the vertex set is represented by D(Λ)*. There is a connection in the form of an edge between two distinct vertices ς and ϱ in AIG(Λ) iff Ann(ςϱ)≠Ann(ς)∩Ann(ϱ). In this work, we begin by categorizing commutative rings Λ, which are finite in structure, so that AIG(Λ) forms a star graph/2-outerplanar graph, and we identify the inner vertex number of AIG(Λ). In addition, a classification of the finite rings where the genus of AIG(Λ) is 2, meaning AIG(Λ) is a double-toroidal graph, is also investigated. Further, we determine Λ, having a crosscap 1 of AIG(Λ), indicating that AIG(Λ) is a projective plane. Finally, we examine the domination number for the annihilator intersection graph and demonstrate that it is at maximum, two.

A new method for community identification is proposed which is founded on the analysis of successive neighborhoods, reached through hierarchical growth from a starting vertex, and on the definition of communities as a subgraph whose number of inner connections is larger than outer connections. In order to determine the precision and speed of the method, it is compared with one of the most popular community identification approaches, namely Girvan and Newman's algorithm. Although the hierarchical growth method is not as precise as Girvan and Newman's method, it is potentially faster than most community finding algorithms.

AbstractA massive of early drug tests indicates that there is some strong inner connections among the bio-medical and pharmacology properties of nanostar dendrimers and their molecular structures. Topological descriptors are presented as fundamentally transforming a molecular graph into a number. There exist various categories of such descriptors particularly those descriptors that based on edge and vertex distances. Topological descriptors are exercised for designing biological, physico-chemical, toxicological, pharmacologic and other characteristics of chemical compounds. In this paper, we study infinite classes of siloxane and POPAM dendrimers and derive their Zagreb eccentricity indices, eccentric-connectivity and total-eccentricity indices.

Let $F$ be a finite field, $n\geqslant 2$ an arbitrary integer, $\mathcal{M}_n(F)$ the set of all $n\times n$ matrices over $F$, and $\mathcal{U}_n^1(F)$ the set of all rank one upper triangular matrices of order $n$. For $\mathcal{S}\subseteq\mathcal{M}_n(F)$, denote $C(\mathcal{S})=\{X\in \mathcal{S} |\ XA=AX \ \hbox{for all}\ A\in \mathcal{S}\}$. The commuting graph of $\mathcal{S}$, denoted by $\Gamma(\mathcal{S})$, is the simple undirected graph with vertex set $\mathcal{S}\setminus C(\mathcal{S})$ in which for every two distinct vertices $A$ and $B$, $A\sim B$ is an edge if and only if $AB=BA$. In this paper, it is shown that any graph automorphism of $\Gamma(\mathcal{U}_n^1(F))$ with $n\geqslant 3$ can be decomposed into the product of an extremal automorphism, an inner automorphism, a field automorphism and a local scalar multiplication.

The main aim of the paper is to give the crossing number of the join product G* + Dn for the connected graph G* of order six consisting of P4 + D1 and of one leaf incident with some inner vertex of the path P4 on four vertices, and where Dn consists of n isolated vertices. In the proofs, it will be extend the idea of the minimum numbers of crossings between two different subgraphs from the set of subgraphs which do not cross the edges of the graph G* onto the set of subgraphs by which the edges of G* are crossed exactly once. Due to the mentioned algebraic topological approach, we are able to extend known results concerning crossing numbers for join products of new graphs. The proofs are done with the help of software that generates all cyclic permutations for a given number k, and creates a new graph COG for calculating the distances between all (k-1)! vertices of the graph. Finally, by adding one edge to the graph G*, we are able to obtain the crossing number of the join product of one other graph with the discrete graph Dn.

Graphs are a powerful tool for data representation in a wide range of domains like social, biological, informational, etc. But their extremely large sizes often makes it computationally infeasible to study the entire graphs. Graph sampling provides a solution by generating smaller subgraphs which are computationally feasible to analyze and can be used to infer the properties of the entire graph. In this work, we develop a high throughput parallel implementation of Totally Induced Edge Sampling (TIES) algorithm on FPGA. Prior research has shown that TIES performs better than other sampling techniques in terms of preserving the topological properties of the original graph, and thus generates better quality subgraphs. The algorithm randomly samples the edges and inserts the corresponding vertices into the sampled vertex set until the desired number of vertices are sampled. Then, the edges connecting the sampled vertices are included in the sampled subgraph. We use multiple parallel pipelines to achieve high throughput and faster graph sampling. The parallel pipelines need to access a global dynamic data structure which contains the vertices sampled thus far. To support this, we develop a novel dynamic hash table data structure which supports parallel accesses in each clock cycle. We vary the number of pipelines, the size of the sampled subgraph and analyze the performance of the design in terms of on-chip FPGA resource utilization, throughput and total execution time. Our design achieves a throughput as high as 2471 Million Edges Per Second (MEPS) and performs 3.6x better than the state-of-the-art multi-core design.

Abstract In the present paper, lattice geometries have been developed and tested for application in internal cooling of gas turbine blades. These geometries are suitable for embedding within a near surface or double wall cooling configuration. Two types of unit cells with variation in number of ligaments and porosity, were used to generate two lattice configurations. The first type of unit cell consisted of six ligaments of 0.5 mm diameter joined at a common vertex situated at the middle. As such, three ligaments were located on each side of the common middle vertex. In addition, the top half of the unit cell was rotated 60 degrees compared to the bottom half of the unit cell. The second type of unit cell was derived from the first type but with four mutually perpendicular ligaments added in the middle plane. Two lattices, referred to as L1 and L2, were obtained by repeating the type 1 and type 2 unit cells, respectively, in both streamwise and spanwise directions. The test coupons consisted of these lattice structures embedded inside a channel of 2.54 mm height, 38.07 mm width and 38.1 mm in length. The coupons were fabricated using Inconel 718 powder through selective laser sintering (SLS) process. The heat transfer and pressure drop performance was evaluated using steady state tests with constant wall temperature boundary condition and for channel Reynolds number ranging from 2,800 to 15,000. In addition, steady state numerical conjugate heat transfer simulations were conducted to obtain a detailed insight into the prevalent flow field and temperature distribution. Experimental results showed a heat transfer enhancement of upto 3 times at the highest Reynolds number compared to a smooth channel. Both the heat transfer and pressure drop increased with a decrease in the porosity from L1 to L2. The numerical results revealed formation of prominent vortical structures in the inter-unit cell spaces. These vortical structures were located in the upper half of the channel causing an increased heat transfer on the top end wall. As a result, these lattice structures provided an augmented heat transfer with a potential for favorable redistribution of the coolant.

Different labyrinth seal configurations are used in modern heavy-duty gas turbine such as see-through stepped or honeycomb seals. The characterization of leakage flow through the seals is one of the main tasks for secondary air system designers as well as the evaluation of increase in temperature due to heat transfer and windage effects. In high temperature turbomachinery applications, knowledge of the heat transfer characteristics of flow leaking through the seals is needed in order to accurately predict seal dimensions and performance as affected by thermal expansion. This paper deals with the influence of clearance on the leakage flow and heat transfer coefficient of a contactless labyrinth seal. A scaled-up planar model of the seal mounted in the inner shrouded vane of the Ansaldo AE94.3A gas turbine has been experimentally investigated. Five clearances were tested using a stationary test rig. The experiments covered a range of Reynolds numbers between 5000 and 40000 and pressure ratios between 1 and 3.3. Local heat transfer coefficients were calculated using a transient technique. It is shown that the clearance/pitch ratio has a significant effect upon both leakage loss and heat transfer coefficient. Hodkinson’s and Vermes’ models are used to fit experimental mass flow rate and pressure drop data. This approach shows a good agreement with experimental data.

Direct methanol fuel cells (DMFCs) are considered as a competitive power source candidate for portable electronic devices. Nafion® has been widely used for the electrolyte of DMFCs because of its good proton conductivity and high chemical and mechanical stability. However, the major problem that must be solved before commercialization is the high methanol crossover through the membrane. There are a number of studies on experiments about the methanol crossover rate through the membrane but only few theoretical investigations have been presented [1–3]. In this paper, an atomistic model [4] is presented to analyze the molecular structure of the electrolyte and dynamic properties of nanofluids at different methanol concentration. In the same time, the nano-scopic phenomenon of methanol crossover through the membrane is observed. The simulation system consists of the Nafion fragments, hydronium ions, water clusters and methanol molecules. Fig. 1 shows the simplified Nafion fragment in our simulation. Both intra- and inter-molecular interactions were involved in this study. Intermolecular interactions include the van der Waals and the electrostatic potentials. Intramolecular interactions consist of bond, angle and dihedral potentials. The force constants used above were determined from the DREIDING force field. The SPC/E model was employed for water molecules. The three-site OPLS potential model was utilized for the intermolecular potential in methanol. Each proton which migrates inside the electrolyte is assumed to combine with one water molecule to form the hydronium (H3O+). The force parameters for the hydronium were taken from Burykin et al [5]. The atomistic simulation was carried out on the software DLPOLY. First, a 500 ps NPT ensemble was performed to make the system reach a proper configuration. This step was followed by another 500 ps NVT simulation. All molecular simulations were performed at a temperature of 323K with three-dimensional periodic boundary conditions. The intermolecular interactions were truncated at 10 Å and the equations of motion were solved using the Verlet scheme with a time step of 1 fs. Fig. 2 shows the calculated density of the simulation system for different methanol concentrations at 323K. It can be seen that the density decreases with the methanol uptakes. The volume of the system increases as the methanol concentration increases, which means that the membrane swelling with methanol uptakes. The radial distribution functions (RDFs) of the ether-like oxygen (O2) toward water and methanol molecules for different methanol concentrations at 323K are shown in Fig. 3. From this figure, we find that methanol molecules can reside in the vicinity of the hydrophobic part of the side chain while water can not. Fig. 4 shows the RDFs between the oxygen atom of the sulfonic acid groups (O3) and solvents for different methanol concentrations at 323K. As shown in Fig. 4, both water and methanol have a tendency to cluster near the sulfonic acid groups, but water molecules prefer to associate with the sulfonic acid groups in comparison with methanol molecules. The mean square displacements (MSDs) of water and methanol molecules for different methanol concentrations at 323K are displayed in Fig. 5. It is shown that MSD curves have a linear tendency, which means both water and methanol molecules are diffusing in the system during the simulation. As the methanol concentration increases, the slope of MSD curve increases for methanol and decreases for water. This indicates higher methanol content constrains the mobility of water molecules but enhances the mobility of methanol molecules that cross the electrolyte. In summary, molecular simulations of the Nafion membrane swollen in different methanol concentrations (0, 11.23, 21.40, 46.92 wt%) at 323K have been carried out. Both methanol migration mechanism and hydronium diffusion phenomenon have been visualized by monitoring the trajectories of the specific species in the system. MSDs are used to evaluate the mobility and shows that the higher the methanol concentration, the greater the tendency of methanol crossover.