scholarly journals List-antimagic labeling of vertex-weighted graphs

2021 ◽  
Vol vol. 23, no. 3 (Graph Theory) ◽  
Author(s):  
Zhanar Berikkyzy ◽  
Axel Brandt ◽  
Sogol Jahanbekam ◽  
Victor Larsen ◽  
Danny Rorabaugh
Keyword(s):  
Oriented Graph ◽  
Weighted Graphs ◽  
Antimagic Labeling ◽  
The Difference ◽  
Edge Labeling

A graph $G$ is $k$-$weighted-list-antimagic$ if for any vertex weighting $\omega\colon V(G)\to\mathbb{R}$ and any list assignment $L\colon E(G)\to2^{\mathbb{R}}$ with $|L(e)|\geq |E(G)|+k$ there exists an edge labeling $f$ such that $f(e)\in L(e)$ for all $e\in E(G)$, labels of edges are pairwise distinct, and the sum of the labels on edges incident to a vertex plus the weight of that vertex is distinct from the sum at every other vertex. In this paper we prove that every graph on $n$ vertices having no $K_1$ or $K_2$ component is $\lfloor{\frac{4n}{3}}\rfloor$-weighted-list-antimagic. An oriented graph $G$ is $k$-$oriented-antimagic$ if there exists an injective edge labeling from $E(G)$ into $\{1,\dotsc,|E(G)|+k\}$ such that the sum of the labels on edges incident to and oriented toward a vertex minus the sum of the labels on edges incident to and oriented away from that vertex is distinct from the difference of sums at every other vertex. We prove that every graph on $n$ vertices with no $K_1$ component admits an orientation that is $\lfloor{\frac{2n}{3}}\rfloor$-oriented-antimagic.

scholarly journals On the spectral distribution of large weighted random regular graphs

2014 ◽  
Vol 03 (04) ◽  
pp. 1450015 ◽  
Author(s):  
Leo Goldmakher ◽  
Cap Khoury ◽  
Steven J. Miller ◽  
Kesinee Ninsuwan
Keyword(s):  
Spectral Distribution ◽  
Regular Graphs ◽  
Weighted Graphs ◽  
Spectral Measures ◽  
Limiting Spectral Distribution ◽  
Random Weights ◽  
Large Trees ◽  
The Difference ◽  
The Relationship ◽  
Limiting Spectral Measure

McKay proved the limiting spectral measures of the ensembles of d-regular graphs with N vertices converge to Kesten's measure as N → ∞. Given a large d-regular graph we assign random weights, drawn from some distribution [Formula: see text], to its edges. We study the relationship between [Formula: see text] and the associated limiting spectral distribution obtained by averaging over the weighted graphs. We establish the existence of a unique "eigendistribution" (a weight distribution [Formula: see text] such that the associated limiting spectral distribution is a rescaling of [Formula: see text]). Initial investigations suggested that the eigendistribution was the semi-circle distribution, which by Wigner's Law is the limiting spectral measure for real symmetric matrices. We prove this is not the case, though the deviation between the eigendistribution and the semi-circular density is small (the first seven moments agree, and the difference in each higher moment is O(1/d2)). Our analysis uses combinatorial results about closed acyclic walks in large trees, which may be of independent interest.

scholarly journals Cartesian Products of Some Regular Graphs Admitting Antimagic Labeling for Arbitrary Sets of Real Numbers

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Yi-Wu Chang ◽  
Shan-Pang Liu
Keyword(s):  
Complete Graphs ◽  
Regular Graphs ◽  
Real Numbers ◽  
Cartesian Products ◽  
Antimagic Labeling ◽  
Edge Labeling

An edge labeling of graph G with labels in A is an injection from E G to A , where E G is the edge set of G , and A is a subset of ℝ . A graph G is called ℝ -antimagic if for each subset A of ℝ with A = E G , there is an edge labeling with labels in A such that the sums of the labels assigned to edges incident to distinct vertices are different. The main result of this paper is that the Cartesian products of complete graphs (except K 1 ) and cycles are ℝ -antimagic.

scholarly journals Tree-Antimagicness of Web Graphs and Their Disjoint Union

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Zhijun Zhang ◽  
Muhammad Awais Umar ◽  
Xiaojun Ren ◽  
Basharat Rehman Ali ◽  
Mujtaba Hussain ◽  
...  
Keyword(s):  
Graph Theory ◽  
Disjoint Union ◽  
Graph Labeling ◽  
Labeled Graph ◽  
Antimagic Labeling ◽  
Research Article ◽  
Web Graphs ◽  
Vertex Set ◽  
Edge Labeling

In graph theory, the graph labeling is the assignment of labels (represented by integers) to edges and/or vertices of a graph. For a graph G=V,E, with vertex set V and edge set E, a function from V to a set of labels is called a vertex labeling of a graph, and the graph with such a function defined is called a vertex-labeled graph. Similarly, an edge labeling is a function of E to a set of labels, and in this case, the graph is called an edge-labeled graph. In this research article, we focused on studying super ad,d-T4,2-antimagic labeling of web graphs W2,n and isomorphic copies of their disjoint union.

scholarly journals Local Antimagic Chromatic Number for Copies of Graphs

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1230
Author(s):  
Martin Bača ◽  
Andrea Semaničová-Feňovčíková ◽  
Tao-Ming Wang
Keyword(s):  
Chromatic Number ◽  
Disjoint Union ◽  
Vertex Coloring ◽  
Vertex Weight ◽  
Antimagic Labeling ◽  
Multiple Copies ◽  
Minimum Number ◽  
Proper Vertex ◽  
Edge Labeling

An edge labeling of a graph G=(V,E) using every label from the set {1,2,⋯,|E(G)|} exactly once is a local antimagic labeling if the vertex-weights are distinct for every pair of neighboring vertices, where a vertex-weight is the sum of labels of all edges incident with that vertex. Any local antimagic labeling induces a proper vertex coloring of G where the color of a vertex is its vertex-weight. This naturally leads to the concept of a local antimagic chromatic number. The local antimagic chromatic number is defined to be the minimum number of colors taken over all colorings of G induced by local antimagic labelings of G. In this paper, we estimate the bounds of the local antimagic chromatic number for disjoint union of multiple copies of a graph.

L(2,1)-Edge-Labelings of the Edge-Path-Replacement of a Graph

2018 ◽  
Vol 29 (01) ◽  
pp. 91-100
Author(s):  
Nianfeng Lin ◽  
Damei Lü ◽  
Jinhua Wang
Keyword(s):  
Maximum Degree ◽  
Common Edge ◽  
Edge Path ◽  
The Difference ◽  
Edge Labeling

Two edges [Formula: see text] and [Formula: see text] in a graph [Formula: see text] are said to be adjacent if they have a vertex in common, and distance two apart if they are nonadjacent but both are adjacent to a common edge. An [Formula: see text]-edge-labeling of a graph [Formula: see text] is an assignment of nonnegative integers, called labels, to the edges of [Formula: see text] such that the difference between labels of any two adjacent edges is at least [Formula: see text], and the labels of any two edges that are distance two apart are different. The span of an [Formula: see text]-edge-labeling of a graph [Formula: see text] is the difference between the maximum and minimum labels. The minimum span over all [Formula: see text]-edge-labelings of a graph [Formula: see text] is called the [Formula: see text]-edge-labeling number of [Formula: see text], denoted by [Formula: see text]. For [Formula: see text], the edge-path-replacement of a graph [Formula: see text], denoted by [Formula: see text], is a graph obtained by replacing each edge of [Formula: see text] with a path [Formula: see text] on [Formula: see text] vertices. This paper investigates the [Formula: see text]-edge-labeling number of the edge-path-replacement [Formula: see text] of a graph [Formula: see text] for [Formula: see text]. We get the following main results: [Formula: see text] Let [Formula: see text] be a graph with maximum degree [Formula: see text] and [Formula: see text] be an integer not less than [Formula: see text], then [Formula: see text] if [Formula: see text] is odd, and otherwise [Formula: see text]. [Formula: see text] Let [Formula: see text] be a graph with maximum degree [Formula: see text]. Then [Formula: see text] when [Formula: see text] is even, and [Formula: see text] when [Formula: see text] is odd.

The Origin of the Moon

1962 ◽  
Vol 14 ◽  
pp. 149-155 ◽  
Author(s):  
E. L. Ruskol
Keyword(s):  
Chemical Composition ◽  
Solar System ◽  
The Moon ◽  
The Earth ◽  
The Difference ◽  
Origin Of The Moon

The difference between average densities of the Moon and Earth was interpreted in the preceding report by Professor H. Urey as indicating a difference in their chemical composition. Therefore, Urey assumes the Moon's formation to have taken place far away from the Earth, under conditions differing substantially from the conditions of Earth's formation. In such a case, the Earth should have captured the Moon. As is admitted by Professor Urey himself, such a capture is a very improbable event. In addition, an assumption that the “lunar” dimensions were representative of protoplanetary bodies in the entire solar system encounters great difficulties.

Influence of Cell Wall Composition on the Fossilisation of Bacteria and the Implications for the Search for Early Life Forms

1997 ◽  
Vol 161 ◽  
pp. 491-504 ◽  
Author(s):  
Frances Westall
Keyword(s):  
Cell Wall ◽  
Life Forms ◽  
Cation Binding ◽  
Positive Bacterium ◽  
Gram Positive ◽  
Gram Positive Bacteria ◽  
Transmission Electron ◽  
Hydrothermal Sediments ◽  
Identification Of Bacteria ◽  
The Difference

AbstractThe oldest cell-like structures on Earth are preserved in silicified lagoonal, shallow sea or hydrothermal sediments, such as some Archean formations in Western Australia and South Africa. Previous studies concentrated on the search for organic fossils in Archean rocks. Observations of silicified bacteria (as silica minerals) are scarce for both the Precambrian and the Phanerozoic, but reports of mineral bacteria finds, in general, are increasing. The problems associated with the identification of authentic fossil bacteria and, if possible, closer identification of bacteria type can, in part, be overcome by experimental fossilisation studies. These have shown that not all bacteria fossilise in the same way and, indeed, some seem to be very resistent to fossilisation. This paper deals with a transmission electron microscope investigation of the silicification of four species of bacteria commonly found in the environment. The Gram positiveBacillus laterosporusand its spore produced a robust, durable crust upon silicification, whereas the Gram negativePseudomonas fluorescens, Ps. vesicularis, andPs. acidovoranspresented delicately preserved walls. The greater amount of peptidoglycan, containing abundant metal cation binding sites, in the cell wall of the Gram positive bacterium, probably accounts for the difference in the mode of fossilisation. The Gram positive bacteria are, therefore, probably most likely to be preserved in the terrestrial and extraterrestrial rock record.

Structuring, Motions and Shapes of Corona Emission Line Profiles

1994 ◽  
Vol 144 ◽  
pp. 421-426
Author(s):  
N. F. Tyagun
Keyword(s):  
Emission Line ◽  
Filling Factor ◽  
Direct Relationship ◽  
Coronal Plasma ◽  
Line Of Sight ◽  
Line Profiles ◽  
The Difference ◽  
Yellow Line ◽  
Red Line

AbstractThe interrelationship of half-widths and intensities for the red, green and yellow lines is considered. This is a direct relationship for the green and yellow line and an inverse one for the red line. The difference in the relationships of half-widths and intensities for different lines appears to be due to substantially dissimilar structuring and to a set of line-of-sight motions in ”hot“ and ”cold“ corona regions.When diagnosing the coronal plasma, one cannot neglect the filling factor - each line has such a factor of its own.

Difference Fourier Analysis of Glucose Embedded and Frozen Hydrated Purple Membrane

1982 ◽  
Vol 40 ◽  
pp. 74-75
Author(s):  
Jules S. Jaffe ◽  
Robert M. Glaeser
Keyword(s):  
Purple Membrane ◽  
Data Set ◽  
High Resolution Data ◽  
X Ray ◽  
X Ray Crystallography ◽  
Fourier Techniques ◽  
Versus Protein ◽  
The Difference ◽  
Difference Fourier ◽  
Ideal Method

Although difference Fourier techniques are standard in X-ray crystallography it has only been very recently that electron crystallographers have been able to take advantage of this method. We have combined a high resolution data set for frozen glucose embedded Purple Membrane (PM) with a data set collected from PM prepared in the frozen hydrated state in order to visualize any differences in structure due to the different methods of preparation. The increased contrast between protein-ice versus protein-glucose may prove to be an advantage of the frozen hydrated technique for visualizing those parts of bacteriorhodopsin that are embedded in glucose. In addition, surface groups of the protein may be disordered in glucose and ordered in the frozen state. The sensitivity of the difference Fourier technique to small changes in structure provides an ideal method for testing this hypothesis.

Destruction of Actin Filaments by Osmium Tetroxide

1977 ◽  
Vol 35 ◽  
pp. 466-467
Author(s):  
P. Maupin-Szamier ◽  
T. D. Pollard
Keyword(s):  
Actin Filaments ◽  
Time Course ◽  
Osmium Tetroxide ◽  
Rabbit Muscle ◽  
Muscle Actin ◽  
Sodium Phosphate Buffer ◽  
Transmission Electron ◽  
The Difference ◽  
Rates Of Decay ◽  
Short Time

We have studied the destruction of rabbit muscle actin filaments by osmium tetroxide (OSO4) to develop methods which will preserve the structure of actin filaments during preparation for transmission electron microscopy.Negatively stained F-actin, which appears as smooth, gently curved filaments in control samples (Fig. 1a), acquire an angular, distorted profile and break into progressively shorter pieces after exposure to OSO4 (Fig. 1b,c). We followed the time course of the reaction with viscometry since it is a simple, quantitative method to assess filament integrity. The difference in rates of decay in viscosity of polymerized actin solutions after the addition of four concentrations of OSO4 is illustrated in Fig. 2. Viscometry indicated that the rate of actin filament destruction is also dependent upon temperature, buffer type, buffer concentration, and pH, and requires the continued presence of OSO4. The conditions most favorable to filament preservation are fixation in a low concentration of OSO4 for a short time at 0°C in 100mM sodium phosphate buffer, pH 6.0.

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