Shadowgraph Research Articles

Perfect matchings in shadow colorings

This birthday note gives a “non-asymptotic” version of our earlier result with G. N. Sarkozy and Szemeredi [3], in which Endre had the lion’s share. A hypergraph H with vertex set V defines the shadow graph G(H) whose vertex set is V and whose edge set is the set of pairs of V that are covered by some hyperedge of H. An edge coloring C of H defines a multicoloring, the shadow coloring $$C^{\prime}$$ on G(H), by assigning all colors of C to an edge xy of G(H) that appear on some edge of H containing $$\{x, y\}$$ . A matching in a graph is a set of pairwise disjoint edges. A matching in a graph is perfect if it covers all vertices of the graph. I show that in every (r −1)-coloring C of the complete r-uniform hypergraph $$K^{r}_{n}$$ there is a monochromatic perfect matching in the shadow coloring $$C^{\prime}$$ (assumingn ≥ r ≥ 2 and n is even).

Linear Incidence Edge Prime Labeling – More Results on Path Related Di Graphs

Objectives: Our aim is to find new families of di graphs that admit linear incidence edge prime labeling. Methods/statistical analysis: Here the vertices are assigned with 0,1,…,m−1 and edges with 2g(v) + g(u), where u is the initial vertex and v is the terminal vertex and g is the vertex labeling function. The graph is prime when the greatest common incidence number of vertices with in degree greater than one is one. Findings: Here we prove that di graph of corona product of Pn with K2, strong shadow graph of path Pn, strong splitting graph of path Pn, square graph of path Pn, tortoise graph of path Pn, graph obtained by joining the corresponding internal vertices of two copies of path Pn, strong Z graph of path Pn admit linear incidence edge prime labeling. Application/improvements: One can generalize these results and find some structural properties. These results may be applied to the transportation problem, chemical graph theory and decision analysis. Keywords: Linear, Incidence, Prime Labeling, Strong Z Graph of Path Pn, Strong Shadow Graph of Path Pn, Strong Splitting Graph of Path Pn.

$t$-Wise Berge and $t$-Heavy Hypergraphs

In many proofs concerning extremal parameters of Berge hypergraphs one starts with analyzing that part of that shadow graph which is contained in many hyperedges. Capturing this phenomenon we intro...

A Research of Achromatic and B-Chromatic Number of Multistar-Related Graphs

The structural properties, achromatic number and b-chromatic number of central graph of double star graph and triple star graph have been studied in [6]. In this paper, these studies have been carried out, for the central graph of any multi star graph and central graph of shadow graph of star graph and double star graph.

Numerical and experimental analysis of the double-diffusive convection in a linearly stratified medium

Introduction: In this paper, we numerically and experimentally studied the onset and the mechanisms of spatiotemporal evolution of the double convective diffusion in a saline medium linearly stratified and heated from below at a constant temperature. Methodology: The numerical simulations were based on the solution of the Navier–Stokes,energy, and concentration equations in stream-vorticity formulation. The numerical method used is the Hermitian compact one. In the experimental studies, a transparent cavity with free surface was filled with linearly stratified solution. The solution was heated from below at a constant temperature. The convective motions were visualized using shadowgraph to obtain more information on density exchange through the interfaces. Furthermore, particle image velocimetry (PIV) is used to measure the time evolution of the velocity field. Results: Flow visualizations by Shadowgraph and PIV allowed the comparison between experimental and numerical results. Conclusion: It was found that a multicellular flow oscillating in space and time mechanisms was observed in both experimental and numerical studies.

Mechanism of Candle Flame Oscillation: Detection of Descending Flow above the Candle Flame

When several candles are bundled together, the size of the combined candle flame oscillates. We carried out observational experiments to understand the mechanism of this oscillation. These were optical imaging, shadow graph imaging, temperature imaging around the oscillating candle flame, and image analysis to obtain the quantitative velocity distribution of the air flow above the candle flame. The experiments detected the descending air flow to the candle flame from the upper area, and showed that the descending air flow is involved with the candle flame oscillation. According to the results, we propose a new mechanism of the candle flame oscillation using the analogy of the cumulonimbus cloud in meteorology.

Cordial Labeling of M-Splitting Graph of a Graph

In this paper, we investigate a condition for a splitting graph of a graph, to be cordial. We have extended the concept of splitting graph to $m$-splitting graph of a graph and proved that the $m$-splitting graph of every cordial graph is cordial. We also prove that the splitting graph of $W_n$ is cordial for all $n\geqslant 3$, splitting graph of $K_n$ is cordial for $ n=t^2$ and $t^2\pm 2 $ and splitting graph of shadow graph of any graph is cordial.

The Achromatic and b-chromatic Number of Shadow Graph of some Graphs

In this research work the achromatic and b-chromatic number of central graph of shadow graph of cycle and that of complete bipartite graph are studied. The achromatic and b-chromatic number of central graph of Shadow graph of star graphs are deduced from the results of the complete bi partite graph.

Experiment on similarity between wake flow field and electromagnetic scattering characteristic of the hypersonic model

The plasma sheath and wake flow of the hypersonic vehicle can affect the electromagnetic scattering characteristics of the reentry targets when they pass through the earth atmosphere at high speed. In order to study the similarity between the wake and the characteristic of the model launched at high velocity, the simulation experiments on the electromagnetic scattering characteristics of the spherical models made of Al2O3 and their wakes are carried out under the same binary scaling parameters in the ballistic range. The models are launched by the two-stage light-gas gun. The diameters of the models are 8 mm, 10 mm, 12 mm and 15 mm, respectively, while the pressures of the target chamber are 6.3 kPa, 5.0 kPa, 4.2 kPa and 3.3 kPa, respectively. The shock standoff distance is obtained by the shadow graph system. The electron density distribution of the wake is measured by the electron density measurement system. The RCS distribution of the wake and the model are acquired by X band monostatic radars, whose visual angle is 40. The results show that the shock standoff distance gradually increases with the increasing of the model dimension under the conditions of the same velocity and binary scaling parameters. The wake electron densities of different models are similar in their variation trends and orders of magnitude. The wake flow field of the different models with high velocity are the same as the results predicted by the double scale laws. The RCS distributions and total RCS of the wake of the models are different from each other. The electromagnetic scattering properties of the wake flow field of the various models do not conform with the predicted results obtained from the double scale law. The electromagnetic scattering energy is distributed over the regions of the models made up of aluminium oxide and the wake zones. There appears to be one center of the electromagnetic scattering energy in the area of the model coated with flow field, while several centers emerge in the region of the wake. The measuring signals of the RCS of the models show a random distribution, because the amplitude variation of the RCS and the frequency change of the RCS are random. The total RCS of the model increases with the increase of the model dimension, but the variation range of ripple frequency decreases with the increase of the model dimension.

In vivo X-Ray Phase Imaging

In vivo X-Ray Phase Imaging

Some Edge Pair Sum Graphs

An injective map f : E(G)→{± 1,±2, … ,±q} is said to be an edge pair sum labeling of a graph G(p, q) if the induced vertex function f* : V(G)→Z − {0} defined by f* (v)=∑e∈Evf(e) is one – one, where Ev denotes the set of edges in G that are incident with a vertex v and f*(V(G)) is either of the form or according as p is even or odd. A graph which admits edge pair sum labeling is called an edge pair sum graph. In this paper we prove that the one point union of cycles, the perfect binary tree, shadow graph, total graph and Pn2 admit edge pair sum labeling.

Hop Domination in Graphs-II

AbstractLet G = (V;E) be a graph. A set S ⊂ V (G) is a hop dominating set of G if for every v ∈ V - S, there exists u ∈ S such that d(u; v) = 2. The minimum cardinality of a hop dominating set of G is called a hop domination number of G and is denoted by γh(G). In this paper we characterize the family of trees and unicyclic graphs for which γh(G) = γt(G) and γh(G) = γc(G) where γt(G) and γc(G) are the total domination and connected domination numbers of G respectively. We then present the strong equality of hop domination and hop independent domination numbers for trees. Hop domination numbers of shadow graph and mycielskian graph of graph are also discussed.

Comments on "electrical breakdown in dielectric liquids-a short overview" by Par Wedin [Letter to the Editors

This interesting publication on today’s knowledge summarizes physical models of electrical breakdown in insulating liquids as published during the last 30 years. Older research activity in this field contributed to the description of the phenomena of partial discharges and breakdown in insulating liquids and its comparison with discharges in gases, especially in air. Thus, at the High-Voltage Laboratory of Dresden Technical University, the breakdown phenomena and mechanisms were intensively investigated using sensitive current pulse measurement and discharge figures (Schlieren method of shadow graphs, photograms and photomultiplier measurements) [1]–[3]. The following supplementary comments are based on these investigations.

Total magic cordial labeling of square and shadow graphs

Total magic cordial labeling of square and shadow graphs

Modular Multiplicative Divisor Labeling of Some Path Related Graphs

A graph G (V,E) with |V| = n is said to have modular multiplicative divisor labeling if there exist a bijection f: V(G) → {1, 2, …,} and the induced function f * : E(G) → {0, 1, 2, …, n - 1} where f(uv) = f(u)f(v) (mod n) such that n divides the sum of all edge labels of G. We prove that the path P n , and the graph P a, b (a graph which connects two vertices by means of "b" internally disjoint paths of length "a" each), shadow graph of a path and the cartesian product P n × P 1 , (n is not a multiple of 6) admits modular multiplicative divisor labeling. Also we discuss the upper bound for the number of edges in a modular multiplicative divisor graphs. AMS Subject Classification: 05C78

Modular Multiplicative Divisor Labeling of Some Path Related Graphs

A graph G (V,E) with |V| = n is said to have modular multiplicative divisor labeling if there exist bijection f: V(G) → {1, 2, …,} and the induced function f * : E(G) → {0, 1, 2, …, n - 1} where f(uv) = f(u)f(v) (mod n) such that n divides the sum of all edge labels of G. We prove that the path P n , and the graph P a, (a graph which connects two vertices by means of b internally disjoint paths of length a each), shadow graph of path and the cartesian product P n × P 1 , (n is not multiple of 6) admits modular multiplicative divisor labeling. Also we discuss the upper bound for the number of edges in modular multiplicative divisor graphs. AMS Subject Classification: 05C78

Time dependency of the laser-induced nanostructuring process of chromium layers with different thicknesses on fused silica

Nanostructures exhibit a raised importance in manifold application fields like electronics and optics. The laser irradiation of thin metal layers allows the fabrication of metal nanostructures induced by a melting and deformation process where the resultant structures are dependent on the laser and metal layer parameters. However, for an optimization of this process a detailed physical understanding is necessary. Therefore, the dynamics of the metal layer deformation process was measured by time-dependent reflection and transmission as well as shadow graph measurements at different KrF excimer laser parameters (laser fluence and number of laser pulses) and metal layer thicknesses were used. Magnetron-sputtered thin chromium films with a thickness from 10 to 100nm on fused silica substrates were studied. Based on the optical measurements the liquid phase lifetime of the metal was estimated and compared with the calculated lifetime using a simple thermodynamic model.

On Square Divisor Cordial Graphs

The square divisor cordial labeling is a variant of cordial labeling and divisor cordial labeling. Here we prove that the graphs like flower Fln, bistar Bn,n, square graph of Bn,n, shadow graph of Bn,n as well as splitting graphs of star Kl,n and bistar Bn,n are square divisor cordial graphs. Moreover we show that the degree splitting graphs of Bn,n and Pn admit square divisor cordial labeling. © 2014 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi: http://dx.doi.org/10.3329/jsr.v6i3.16412 J. Sci. Res. 6 (3), 445-455 (2014)

Some New even Harmonious Graphs

Let $G(V,E)$ be a graph with $p$ vertices and $q$ edges. A function $f$ is called even harmonious labeling of a graph $G(V, E)$ if $f : V \rightarrow \{0, 1, 2, \dots , 2q\}$ is injective and the induced function $f^* : E \rightarrow \{0, 2, 4, \dots , 2(q - 1)\}$ defined as $f^*(uv) = (f(u) + f(v)) ~(mod~ 2q )$ is bijective. In this paper we establish an even harmonious labeling for the graphs $C_n \odot mK_1$($n$ is odd), $P_n \odot mK_1$($n$ is odd), $C_n @ K_1$ ($n$ is even), $P_n$ ($n$ is even) with $n - 1$ copies of $mK_1$, the shadow graph $D_2(K_1, n)$ and the splitting graph $spl(K_1,n)$.

Cordial Labeling for some Bistar Related Graphs

In this paper we prove that square graph and shadow graph of bistar admit cordial labeling. Moreover we prove that splitting graph of bistar as well as degree splitting graph of bistar are cordial graphs.