scholarly journals Total Face Irregularity Strength of Grid and Wheel Graph under K-Labeling of Type (1, 1, 0)

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Aleem Mughal ◽  
Noshad Jamil
Keyword(s):  
Plane Graph ◽  
Plane Graphs ◽  
Wheel Graph ◽  
Wheel Graphs ◽  
The Face ◽  
Vertex Set ◽  
Positive Integers ◽  
Special Case ◽  
Irregularity Strength

In this study, we used grids and wheel graphs G = V , E , F , which are simple, finite, plane, and undirected graphs with V as the vertex set, E as the edge set, and F as the face set. The article addresses the problem to find the face irregularity strength of some families of generalized plane graphs under k -labeling of type α , β , γ . In this labeling, a graph is assigning positive integers to graph vertices, graph edges, or graph faces. A minimum integer k for which a total label of all verteices and edges of a plane graph has distinct face weights is called k -labeling of a graph. The integer k is named as total face irregularity strength of the graph and denoted as tfs G . We also discussed a special case of total face irregularity strength of plane graphs under k -labeling of type (1, 1, 0). The results will be verified by using figures and examples.

scholarly journals On the Total Vertex Irregular Labeling of Proper Interval Graphs

2020 ◽  
Vol 12 (4) ◽  
pp. 537-543
Author(s):  
A. Rana
Keyword(s):  
Efficient Algorithm ◽  
Simple Graph ◽  
Interval Graphs ◽  
Vertex Weight ◽  
Vertex Set ◽  
Positive Integers ◽  
Irregularity Strength

A labeling of a graph is a mapping that maps some set of graph elements to a set of numbers (usually positive integers).  For a simple graph G = (V, E) with vertex set V and edge set E, a labeling  Φ: V ∪ E → {1, 2, ..., k} is called total k-labeling. The associated vertex weight of a vertex x∈ V under a total k-labeling  Φ is defined as wt(x) = Φ(x) + ∑y∈N(x) Φ(xy) where N(x) is the set of neighbors of the vertex x. A total k-labeling is defined to be a vertex irregular total labeling of a graph, if for every two different vertices x and y of G, wt(x)≠wt(y). The minimum k for which  a graph G has a vertex irregular total k-labeling is called the total vertex irregularity strength of G, tvs(G). In this paper, total vertex irregularity strength of interval graphs is studied. In particular, an efficient algorithm is designed to compute tvs of proper interval graphs and bounds of tvs is presented for interval graphs.

EMBEDDING POINT SETS INTO PLANE GRAPHS OF SMALL DILATION

2007 ◽  
Vol 17 (03) ◽  
pp. 201-230 ◽  
Author(s):  
ANNETTE EBBERS-BAUMANN ◽  
ANSGAR GRÜNE ◽  
ROLF KLEIN ◽  
MAREK KARPINSKI ◽  
CHRISTIAN KNAUER ◽  
...  
Keyword(s):  
Plane Graph ◽  
Upper And Lower Bounds ◽  
Convex Curve ◽  
Embedding Problem ◽  
Finite Point ◽  
Plane Graphs ◽  
Parallel Lines ◽  
Vertex Set ◽  
Point Set ◽  
Set Of Points

Let S be a set of points in the plane. What is the minimum possible dilation of all plane graphs that contain S? Even for a set S as simple as five points evenly placed on the circle, this question seems hard to answer; it is not even clear if there exists a lower bound > 1. In this paper we provide the first upper and lower bounds for the embedding problem. 1. Each finite point set can be embedded into the vertex set of a finite triangulation of dilation ≤ 1.1247. 2. Each embedding of a closed convex curve has dilation ≥ 1.00157. 3. Let P be the plane graph that results from intersecting n infinite families of equidistant, parallel lines in general position. Then the vertex set of P has dilation [Formula: see text].

scholarly journals Longest paths in random Apollonian networks and largest r-ary subtrees of random d-ary recursive trees

2016 ◽  
Vol 53 (3) ◽  
pp. 846-856 ◽  
Author(s):  
Andrea Collevecchio ◽  
Abbas Mehrabian ◽  
Nick Wormald
Keyword(s):  
Related Result ◽  
Plane Graph ◽  
Time Step ◽  
Single Vertex ◽  
Planar Triangulation ◽  
The Face ◽  
Longest Paths ◽  
Recursive Trees ◽  
Positive Integers ◽  
Iterative Construction

AbstractLet r and d be positive integers with r<d. Consider a random d-ary tree constructed as follows. Start with a single vertex, and in each time-step choose a uniformly random leaf and give it d newly created offspring. Let 𝒯d,t be the tree produced after t steps. We show that there exists a fixed δ<1 depending on d and r such that almost surely for all large t, every r-ary subtree of 𝒯d,t has less than tδ vertices. The proof involves analysis that also yields a related result. Consider the following iterative construction of a random planar triangulation. Start with a triangle embedded in the plane. In each step, choose a bounded face uniformly at random, add a vertex inside that face and join it to the vertices of the face. In this way, one face is destroyed and three new faces are created. After t steps, we obtain a random triangulated plane graph with t+3 vertices, which is called a random Apollonian network. We prove that there exists a fixed δ<1, such that eventually every path in this graph has length less than t𝛿, which verifies a conjecture of Cooper and Frieze (2015).

scholarly journals Gaps in the Chromatic Spectrum of Face-Constrained Plane Graphs

10.37236/1588 ◽  
2001 ◽  
Vol 8 (1) ◽  
Author(s):  
Daniel Kobler ◽  
André Kündgen
Keyword(s):  
Plane Graph ◽  
Plane Graphs ◽  
The Face ◽  
Chromatic Spectrum

Let $G$ be a plane graph whose vertices are to be colored subject to constraints on some of the faces. There are 3 types of constraints: a $C$ indicates that the face must contain two vertices of a $C$ommon color, a $D$ that it must contain two vertices of a $D$ifferent color and a $B$ that $B$oth conditions must hold simultaneously. A coloring of the vertices of $G$ satisfying the facial constraints is a strict $k$-coloring if it uses exactly $k$ colors. The chromatic spectrum of $G$ is the set of all $k$ for which $G$ has a strict $k$-coloring. We show that a set of integers $S$ is the spectrum of some plane graph with face-constraints if and only if $S$ is an interval $\{s,s+1,\dots,t\}$ with $1\leq s\leq 4$, or $S=\{2,4,5,\dots,t\}$, i.e. there is a gap at 3.

Evidence for a shear mechanism for the precipitation of γ-zirconium hydride in zirconium

1978 ◽  
Vol 36 (1) ◽  
pp. 658-659
Author(s):  
G.J.C. Carpenter
Keyword(s):  
Elevated Temperature ◽  
Strain Field ◽  
Zirconium Hydride ◽  
Zirconium Atom ◽  
Atom Diffusion ◽  
Solvus Temperature ◽  
Hexagonal Close Packed ◽  
Partial Dislocations ◽  
The Face

In zirconium-hydrogen alloys, rapid cooling from an elevated temperature causes precipitation of the face-centred tetragonal (fct) phase, γZrH, in the form of needles, parallel to the close-packed <1120>zr directions (1). With low hydrogen concentrations, the hydride solvus is sufficiently low that zirconium atom diffusion cannot occur. For example, with 6 μg/g hydrogen, the solvus temperature is approximately 370 K (2), at which only the hydrogen diffuses readily. Shears are therefore necessary to produce the crystallographic transformation from hexagonal close-packed (hep) zirconium to fct hydride.The simplest mechanism for the transformation is the passage of Shockley partial dislocations having Burgers vectors (b) of the type 1/3<0110> on every second (0001)Zr plane. If the partial dislocations are in the form of loops with the same b, the crosssection of a hydride precipitate will be as shown in fig.1. A consequence of this type of transformation is that a cumulative shear, S, is produced that leads to a strain field in the surrounding zirconium matrix, as illustrated in fig.2a.

Studying Infection Worries by Ecological Momentary Assessment: Development and Causal Factors in Sweden during the Early Phase of the Covid-19 Pandemic (Preprint)

2020 ◽  
Author(s):  
Peter Schulz ◽  
Elin Andersson ◽  
Nicole Bizzotto ◽  
Margareta Norberg
Keyword(s):  
Study Design ◽  
Preventive Action ◽  
Causal Factors ◽  
Perceived Severity ◽  
Assessment Development ◽  
Infection Susceptibility ◽  
The Face ◽  
New Type ◽  
Ecological Momentary ◽  
Special Case

BACKGROUND The foray of Covid-19 around the globe is sure to have instigated worries in many humans, and lockdown measures may well have created their own worries. Sweden, in contrast to most other countries, had first relied on voluntary measures, but had to change its policy in the face of an increasing number of infections. OBJECTIVE The aim was to better understand the worried reactions to the virus and the lockdown measures. To grasp the reactions, their development over time was studied. METHODS Results were based on an unbalanced panel sample of 261 Swedish participants filling in 3218 interview questionnaires by smartphone in a 7-week period in 2020. Causal factors considered in this study include the perceived severity of an infection, the susceptibility of a person to the threat posed by the virus, the perceived efficacy of safeguarding measures and the assessment of government action against the spread of Covid-19. The effect of these factors on worries was traced in two analytical steps: the effects at the beginning of the study, and the effect on the trend during the study. RESULTS Findings confirmed that the hypothesized causal factors (severity of infection, susceptibility to the threat of the virus, efficacy of safeguarding and the assessment of government preventive action did indeed affect worries. CONCLUSIONS The results confirmed earlier research in a very special case and demonstrated the usefulness of a different study design, which takes a longitudinal perspective, and a new type of data analysis borrowed from multi-level study design.

scholarly journals The Irregularity and Modular Irregularity Strength of Fan Graphs

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 605
Author(s):  
Martin Bača ◽  
Zuzana Kimáková ◽  
Marcela Lascsáková ◽  
Andrea Semaničová-Feňovčíková
Keyword(s):  
Simple Graph ◽  
Isolated Vertex ◽  
Positive Integers ◽  
Irregularity Strength

For a simple graph G with no isolated edges and at most, one isolated vertex, a labeling φ:E(G)→{1,2,…,k} of positive integers to the edges of G is called irregular if the weights of the vertices, defined as wtφ(v)=∑u∈N(v)φ(uv), are all different. The irregularity strength of a graph G is known as the maximal integer k, minimized over all irregular labelings, and is set to ∞ if no such labeling exists. In this paper, we determine the exact value of the irregularity strength and the modular irregularity strength of fan graphs.

Management of a Large Arteriovenous Fistula in the Face: A Case of Neurofibromatosis Type 1

1997 ◽  
Vol 39 (3) ◽  
pp. 308-313 ◽  
Author(s):  
Mustafa Yilmaz ◽  
Emel Ada ◽  
Haluk Vayvada ◽  
Ali Barutçu
Keyword(s):  
Arteriovenous Fistula ◽  
Neurofibromatosis Type 1 ◽  
Neurofibromatosis Type ◽  
The Face

GENERA OF THE LINKS DERIVED FROM 2-CONNECTED PLANE GRAPHS

2012 ◽  
Vol 21 (14) ◽  
pp. 1250129 ◽  
Author(s):  
SHUYA LIU ◽  
HEPING ZHANG
Keyword(s):  
Explicit Formula ◽  
Large Family ◽  
Plane Graph ◽  
Plane Graphs ◽  
Degree Sum ◽  
Oriented Link

In this paper, we associate a plane graph G with an oriented link by replacing each vertex of G with a special oriented n-tangle diagram. It is shown that such an oriented link has the minimum genus over all orientations of its unoriented version if its associated plane graph G is 2-connected. As a result, the genera of a large family of unoriented links are determined by an explicit formula in terms of their component numbers and the degree sum of their associated plane graphs.

Anatomic patterning in the expression of vestibulosympathetic reflexes

2000 ◽  
Vol 279 (1) ◽  
pp. R109-R117 ◽  
Author(s):  
I. A. Kerman ◽  
B. J. Yates ◽  
R. M. McAllen
Keyword(s):  
Relative Proportion ◽  
Vestibular Stimulation ◽  
Nerve Fibers ◽  
Spike Shape ◽  
The Face ◽  
Nerve Fascicle ◽  
The Difference ◽  
Vestibulosympathetic Reflexes

To investigate the possibility that expression of vestibulosympathetic reflexes (VSR) is related to a nerve's anatomic location rather than its target organ, we compared VSR recorded from the same type of postganglionic fiber [muscle vasoconstrictor (MVC)] located at three different rostrocaudal levels: hindlimb, forelimb, and face. Experiments were performed on chloralose-anesthetized cats, and vestibular afferents were stimulated electrically. Single MVC unit activity was extracted by spike shape analysis of few-fiber recordings, and unit discrimination was confirmed by autocorrelation. Poststimulus time histogram analysis revealed that about half of the neurons were initially inhibited by vestibular stimulation (type 1 response), whereas the other MVC fibers were initially strongly excited (type 2 response). MVC units with types 1 and 2 responses were present in the same nerve fascicle. Barosensitivity was equivalent in the two groups, but fibers showing type 1 responses fired significantly faster than those giving type 2 responses (0.29 ± 0.04 vs. 0.20 ± 0.02 Hz). Nerve fibers with type 1 responses were most common in the hindlimb (21 of 29 units) and least common in the face (2 of 11 units), the difference in relative proportion being significant ( P < 0.05, χ2 test). These results support the hypothesis that VSR are anatomically patterned.

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