Number Of Subdivisions Research Articles

Roman domination subdivision number of graphs

A Roman dominating function on a graph G = (V, E) is a function \(f : V \rightarrow \{0, 1, 2\}\) satisfying the condition that every vertex v for which f(v) = 0 is adjacent to at least one vertex u for which f(u) = 2. The weight of a Roman dominating function is the value \(w(f) = \sum_{v\in V} f(v)\). The Roman domination number of a graph G, denoted by \(_{\gamma R}(G)\), equals the minimum weight of a Roman dominating function on G. The Roman domination subdivision number \(sd_{\gamma R}(G)\) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the Roman domination number. In this paper, first we establish upper bounds on the Roman domination subdivision number for arbitrary graphs in terms of vertex degree. Then we present several different conditions on G which are sufficient to imply that \(1 \leq sd_{\gamma R}(G) \leq 3\). Finally, we show that the Roman domination subdivision number of a graph can be arbitrarily large.

Paired-Domination Subdivision Numbers of Graphs

A paired-dominating set of a graph G = (V, E) with no isolated vertex is a dominating set of vertices whose induced subgraph has a perfect matching. The paired-domination number of G, denoted by γ pr (G), is the minimum cardinality of a paired-dominating set of G. The paired-domination subdivision number sd γpr (G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the paired-domination number. In this paper we establish upper bounds on the paired-domination subdivision number and pose some problems and conjectures.

An Upper Bound for the Total Domination Subdivision Number of a Graph

A set S of vertices of a graph G = (V, E) without isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination number γ t (G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number $${{\rm sd}_{\gamma_t}(G)}$$ is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the total domination number. In this paper, we prove that $${{\rm sd}_{\gamma_t}(G)\leq 2\gamma_t(G)-1}$$for every simple connected graph G of order n ≥ 3.

Analysis of solving multimode-coupled equations and its improvement for modulated fiber Bragg gratings

An efficient numerical method to solve multimode-coupled equations with two point boundary conditions is improved. Our method [Abrishamian et al., Opt. Fiber Technol.13, 32-38 (2007)] based on theoretical matrix integration of coupled differential equations and then solving the system of equations by use of initial or final conditions would be straightforward and thus beneficial in comparison with previously used fundamental matrix methods that depend strongly on the initial guess. However, we found that the new analysis depends on how accurately the integrals of the matrix element are calculated. For accuracy in the matrix integration it is required to divide the system of equations into a large number of subsections. Then, the reflectivity calculated is found to be comparable to experimental data reported so far. The present method is highly applicable for simulation of any type of fiber Bragg gratings modulated by long period gratings.

Resources for Research on Analogy: A Multi-disciplinary Guide

Work on analogy has been done from a number of disciplinary perspectives throughout the history of Western thought. This work is a multidisciplinary guide to theorizing about analogy. It contains 1,406 references, primarily to journal articles and monographs, and primarily to English language material. classical through to contemporary sources are included. The work is classified into eight different sections (with a number of subsections). A brief introduction to each section is provided. Keywords and key expressions of importance to research on analogy are discussed in the introductory material. Electronic resources for conducting research on analogy are listed as well.

Free-Breathing Accelerated Gadolinium-Enhanced MR Angiography in the Diagnosis of Renovascular Disease

The purpose of this study was to assess the feasibility and accuracy of accelerated free-breathing and breath-hold gadolinium-enhanced MR angiography of the main renal arteries compared with digital subtraction angiography. Renal MR angiograms and catheter angiograms of 47 patients (19 men, 28 women; mean age, 68.1 +/- 15.1 years; range, 28-86 years) were reviewed. Thirty-one of the patients underwent free-breathing and 16 underwent breath-hold MR angiography with the same accelerated multiphase imaging protocol. Images were analyzed for examination quality, percentage narrowing of the main renal artery, and visibility of the branches. Diagnostic values of MR angiography were calculated with catheter angiography as the standard of reference. Sixty-five arteries, 24 of which (37%) had > 49% narrowing, were evaluated in the free-breathing group, and 37 arteries, six of which (16%) had > 49% narrowing, were evaluated in the breath-hold group. Comparison with digital subtraction angiography showed 100% (24/24) sensitivity and 95% (39/41) specificity for > 49% renal artery stenosis and 88% sensitivity (15/17) and 100% (48/48) specificity for > 74% renal artery stenosis in the free-breathing group. In the breath-hold group, sensitivity was 100% (6/6) and specificity 97% (30/31) for > 49% renal artery stenosis, and sensitivity was 100% (5/5) and specificity 100% (32/32) for > 74% renal artery stenosis. None of the examinations was nondiagnostic for the main renal arteries, but a smaller number of visible arterial tree subdivisions were found in the free-breathing group (average, 3.64 per patient) than in the breath-hold group (average, 5.87 per patient) (p = 0.035). Like breath-hold examinations, accelerated free-breathing MR angiographic examinations are feasible and accurate in evaluation of the main renal arteries.

Bounding the total domination subdivision number of a graph in terms of its order

The total domination subdivision number $\mathrm{sd}_{\gamma _{t}}(G)$ of a graph G is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the total domination number. In this paper we prove that $\mathrm{sd}_{\gamma_{t}}(G)\leq \lfloor\frac{2n}{3}\rfloor$ for any simple connected graph G of order n?3 other than K 4. We also determine all simple connected graphs G with $\mathrm{sd}_{\gamma_{t}}(G)=\lfloor\frac{2n}{3}\rfloor$ .

A New Bound on the Total Domination Subdivision Number

A set S of vertices of a graph G = (V, E) without isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination number γt (G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number $$sd_{\gamma_{t}}(G)$$is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the total domination number. In this paper we prove that for every simple connected graph G of order n ≥ 3, $${\rm sd}_{\gamma_{t}}(G)\le 3 +{\rm min}\{d_2(v); v\in V \, {\rm and}\, d(v)\ge 2\}$$.

Ascending and descending regions of a discrete Morse function

We present an algorithm which produces a decomposition of a regular cellular complex with a discrete Morse function analogous to the Morse–Smale decomposition of a smooth manifold with respect to a smooth Morse function. The advantage of our algorithm compared to similar existing results is that it works, at least theoretically, in any dimension. Practically, there are dimensional restrictions due to the size of cellular complexes of higher dimensions, though. We prove that the algorithm is correct in the sense that it always produces a decomposition into descending and ascending regions of the critical cells in a finite number of steps, and that, after a finite number of subdivisions, all the regions are topological disks. The efficiency of the algorithm is discussed and its performance on several examples is demonstrated.

On the total domination subdivision number in some classes of graphs

A set S of vertices of a graph G=(V,E) without isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination numberγt(G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number\(\mathrm {sd}_{\gamma_{t}}(G)\) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the total domination number. In this paper we prove that \(\mathrm {sd}_{\gamma_{t}}(G)\leq\gamma_{t}(G)+1\) for some classes of graphs.

A Simple Method for Design of Adaptive Filters for Sinusoidal Signals

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Filtering of input signals in algorithms for measurement of power system electrical parameters is very important. Filters are used to minimize the noise effect and eliminate the presence of higher order harmonics. In addition to that, a number of measurement algorithms apply orthogonal signal components obtained by two orthogonal finite-impulse response filters. The frequency response of the filters must have nulls at the higher order harmonic frequencies that are expected to be present in the signal and must have a unity gain at the main harmonic frequency. In the case of a time-varying frequency, the filter parameters have to be adapted during frequency estimation. In this paper, a simple method for online design of digital filters for sinusoidal signals is proposed. It is based on closed-form solutions for calculating filter coefficients. A simple linear algorithm for frequency estimation was used, and a derived algorithm for online adaptation of the filter coefficients is computationally very efficient. The number of subsections in the cascade and data window lengths can also be changed, depending on the frequency variations during measurement. </para>

Perfect Matchings and K 4 3 -Tilings in Hypergraphs of Large Codegree

For a k-graph F, let t l (n, m, F) be the smallest integer t such that every k-graph G on n vertices in which every l-set of vertices is included in at least t edges contains a collection of vertex-disjoint F-subgraphs covering all but at most m vertices of G. Let K m k denote the complete k-graph on m vertices. The function $$t_{k-1} (kn, 0, K_k^k)$$(i.e. when we want to guarantee a perfect matching) has been previously determined by Kuhn and Osthus [9] (asymptotically) and by Rodl, Rucinski, and Szemeredi [13] (exactly). Here we obtain asymptotic formulae for some other l. Namely, we prove that for any $$k \ge 4$$and $$k/2 \le l \le k-2$$, $$ t_l(kn, 0, K_k^k) = \left(\frac{1}{2} + o(1)\right) {kn\choose k-l} $$is adjacent to some vertex in S. The domination number γ(G) is the minimum cardinality of a dominating set of G. The domination subdivision number sdγ(G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the domination number. Haynes et al. (Discussiones Mathematicae Graph Theory 21 (2001) 239-253) conjectured that $${\rm sd}_{\gamma} (G) \le \delta(G) + 1$$for any graph G with $$\delta(G) \ge 2$$. In this note we first give a counterexample to this conjecture in general and then we prove it for a particular class of graphs.

Disproof of a Conjecture on the Subdivision Domination Number of a Graph

A set S of vertices of a graph G = (V,E) is a dominating set if every vertex of $$V(G) \setminus S$$ is adjacent to some vertex in S. The domination number γ(G) is the minimum cardinality of a dominating set of G. The domination subdivision number sdγ(G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the domination number. Haynes et al. (Discussiones Mathematicae Graph Theory 21 (2001) 239-253) conjectured that $${\rm sd}_{\gamma} (G) \le \delta(G) + 1$$ for any graph G with $$\delta(G) \ge 2$$. In this note we first give a counterexample to this conjecture in general and then we prove it for a particular class of graphs.

Two-center overlap integrals, three dimensional adaptive integration, and prolate ellipsoidal coordinates

Numerical, adaptive algorithm evaluating the overlap integrals between the Numerical Type Orbitals (NTO) is presented. The described algorithm exploits the properties of the prolate ellipsoidal coordinates, which are the natural choice for two-center overlap integrals. The algorithm is designed for numerical atomic orbitals with the finite support. Since the cusp singularity of the atomic orbitals vanish in the prolate ellipsoidal coordinate system, the adaptive integration algorithm in \({\mathbb{R}^3}\) generates small number of subdivisions. The efficiency and reliability of the algorithm is demonstrated for the overlap integrals evaluated for the selected pairs of Slater Type Orbitals (STO).

One-dimensional finite element heat transfer solution of a fin with triangular perforations of bases parallel and towered its base

Heat transfer dissipation from a horizontal rectangular fin embedded with equilateral triangular perforations is computed numerically using one-dimensional finite element technique. The bases of the triangles are parallel and toward the fin base. The body of the fin is discretized into a number of subdivisions (finite elements). The number of these elements can be altered as required according to the automatic mesh generation. The heat dissipation of the perforated fin is computed and compared with that of the solid one of the same dimensions and same thermal properties. The comparison refers to acceptable results and heat dissipation enhancement due to certain perforation.

Quench Protection for the MICE Cooling Channel Coupling Magnet

This paper describes the passive quench protection system selected for the muon ionization cooling experiment (MICE) cooling channel coupling magnet. The MICE coupling magnet will employ two methods of quench protection simultaneously. The most important method of quench protection in the coupling magnet is the subdivision of the coil. Cold diodes and resistors are put across the subdivisions to reduce both the voltage to ground and the hot-spot temperature. The second method of quench protection is quench-back from the mandrel, which speeds up the spread of the normal region within the coils. Combining quench back with coil subdivision will reduce the hot spot temperature further. This paper explores the effect on the quench process of the number of coil sub-divisions, the quench propagation velocity within the magnet, and the shunt resistance.

Domination subdivision numbers of trees

A set S of vertices of a graph G = ( V , E ) is a dominating set if every vertex of V ( G ) ∖ S is adjacent to some vertex in S . The domination number γ ( G ) is the minimum cardinality of a dominating set of G . The domination subdivision number sd γ ( G ) is the minimum number of edges that must be subdivided in order to increase the domination number. Velammal showed that for any tree T of order at least 3, 1 ≤ sd γ ( T ) ≤ 3 . In this paper, we give two characterizations of trees whose domination subdivision number is 3 and a linear algorithm for recognizing them.

On the Packing Chromatic Number of Trees, Cartesian Products and Some Infinite Graphs

Abstract A subset A of vertices in a graph G is an r-packing if the distance between every pair of distinct vertices in A is more than r. The packing chromatic number, χ ρ ( G ) , is the smallest k for which there exists some partition V 1 , V 2 , … , V k of the vertex set of G such that V r is an r-packing. We obtain lower and upper bounds for the packing chromatic number of Cartesian products and subdivisions of finite graphs and study the existence of monotone colorings in trees. The infinite, planar triangular lattice and the three dimensional square lattice are shown to have unbounded packing chromatic number.

A New Species of Oswaldocruzia (Molineidae: Nematoda) in Chaunus marinus (Amphibian: Bufonidae) (Linneaus, 1758) from Brazil

Oswaldocruzia belenensis n. sp. (Strongylida: Molineidae) from the small intestine of Chaunus marinus (L.) from Belém, Pará State, Brazil is described and illustrated by light and scanning electron microscopy. Oswaldocruzia belenensis n. sp. is a neotropical species of this genus, harboring caudal bursa Type II, spicules divided in 3 branches, i.e., a blade, shoe, and fork. The blade is divided in 4 points, of which at least 2 are bifurcated. Cervical alae are absent; there is a simple cephalic vesicle and synlophe with low ridges perpendicular to the body without chitinous supports. The most closely related species are O. bonsi and O. lescurei. Oswaldocruzia belenensis n. sp. differs from O. lescurei and O. bonsi by the number and location of cephalic papillae, rays 2-3 and 5-6 running parallel and slightly separated, ray 6 not overlapping ray 8, and body structure morphometry. Oswaldocruzia belenensis n sp. also differs from O. lescurei by the discontinuity of the longitudinal ridges, the number of subdivisions of the blade, and the absence of extra processes at the bifurcation level of the fork of the spicules. The new species differs from O. bonsi by male and female body dimensions, the symmetry of the caudal bursa, dimension and subdivisions of the spicules without extra processes of the fork, 2 extra processes at the distal division of the blade, and location of ray 7 at the anterior margin of the cloacal aperture. Oswaldocruzia belenensis n. sp. represents the 82nd species assigned to the genus.

2-Domination Subdivision Number of Graphs

In a graph G, a vertex dominates itself and its neighbors. A subset S ⊆ V(G) is a 2-dominating set of G if S dominates every vertex of V(G) \\ S at least twice. The 2-domination number γ2(G) is the minimum cardinality of a 2-dominating set of G. The 2-domination subdivision number sdγ2(G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the 2-domination number. In this paper, we establish upper bounds on the 2-domination subdivision number for arbitrary graphs in terms of vertex degree and for several graph classes. Then we present some conditions on G which are sufficient to imply that sdγ2(G) = 1.