Arc-transitive abelian regular covering graphs

2016 ◽  
Vol 26 (07) ◽  
pp. 1369-1393 ◽  
Author(s):  
Jicheng Ma
Keyword(s):  
Complete Graph ◽  
Abelian Groups ◽  
Cubic Graphs ◽  
New Approach ◽  
Regular Covering ◽  
Symmetric Graphs

A lot of attention has been paid recently to the construction of symmetric covers of symmetric graphs. After a new approach given by Conder and the author [Arc-transitive abelian regular covers of cubic graphs, J. Algebra 387 (2013) 215–242], the group of covering transformations can be extended to more general abelian groups rather than cyclic or elementary abelian groups. In this paper, by using the Conder–Ma approach, we investigate the symmetric covers of 4-valent symmetric graphs. As an application, all the arc-transitive abelian regular covers of the 4-valent complete graph [Formula: see text] which can be obtained by lifting the arc-transitive subgroups of automorphisms [Formula: see text] and [Formula: see text] are classified.

scholarly journals Arc-Transitive Dihedral Regular Covers of Cubic Graphs

10.37236/4035 ◽  
2014 ◽  
Vol 21 (3) ◽  
Author(s):  
Jicheng Ma
Keyword(s):  
Transformation Group ◽  
Petersen Graph ◽  
Cubic Graphs ◽  
Regular Covering ◽  
Symmetric Graphs ◽  
Cyclic Covers ◽  
Covering Projection

A regular covering projection is called dihedral or abelian if the covering transformation group is dihedral or abelian. A lot of work has been done with regard to the classification of arc-transitive abelian (or elementary abelian, or cyclic) covers of symmetric graphs. In this paper, we investigate arc-transitive dihedral regular covers of symmetric (arc-transitive) cubic graphs. In particular, we classify all arc-transitive dihedral regular covers of $K_4$, $K_{3,3}$, the 3-cube $Q_3$ and the Petersen graph.

RECURSIVE SAMPLING OF PLANAR GRAPHS AND FRACTAL PROPERTIES OF A TWO-DIMENSIONAL QUANTUM GRAVITY

1990 ◽  
Vol 01 (01) ◽  
pp. 165-179 ◽  
Author(s):  
MICHAEL E. AGISHTEIN ◽  
ALEXANDER A. MIGDAL
Keyword(s):  
Monte Carlo ◽  
Random Graphs ◽  
Planar Graphs ◽  
Two Dimensional ◽  
Cubic Graphs ◽  
New Approach ◽  
Standard Methods ◽  
Fractal Properties ◽  
Dimensional Gravity ◽  
Dynamical Triangulation

We describe a new approach to the Monte-Carlo simulations of two-dimensional gravity. Standard dynamical triangulation technique was combined with results of direct enumeration of the cubic graphs. As a result we were able to build large (128K vertices) statistically independent random graphs directly. The quantitative correspondence between our results and those obtained by standard methods has been observed. The algorithm proved to be so efficient that we were able to conduct all the simulations, which usually require the most powerful computers, on an Iris workstation. An opportunity to generate large random graphs allowed us to observe that the internal geometry of random surfaces is more complicated than simple fractals. External geometry also proved to be rather peculiar.

scholarly journals Cubic symmetric graphs of order twice an odd prime-power

2006 ◽  
Vol 81 (2) ◽  
pp. 153-164 ◽  
Author(s):  
Yan-Quan Feng ◽  
Jin Ho Kwak
Keyword(s):  
Automorphism Group ◽  
Cayley Graph ◽  
Prime Power ◽  
Symmetric Graph ◽  
Cubic Graphs ◽  
Full Automorphism Group ◽  
Symmetric Graphs ◽  
Regular Subgroup

AbstractAn automorphism group of a graph is said to be s-regular if it acts regularly on the set of s-arcs in the graph. A graph is s-regular if its full automorphism group is s-regular. For a connected cubic symmetric graph X of order 2pn for an odd prime p, we show that if p ≠ 5, 7 then every Sylow p-subgroup of the full automorphism group Aut(X) of X is normal, and if p ≠3 then every s-regular subgroup of Aut(X) having a normal Sylow p-subgroup contains an (s − 1)-regular subgroup for each 1 ≦ s ≦ 5. As an application, we show that every connected cubic symmetric graph of order 2pn is a Cayley graph if p > 5 and we classify the s-regular cubic graphs of order 2p2 for each 1≦ s≦ 5 and each prime p. as a continuation of the authors' classification of 1-regular cubic graphs of order 2p2. The same classification of those of order 2p is also done.

scholarly journals CUBIC EDGE-TRANSITIVE GRAPHS OF ORDER 8p2

2008 ◽  
Vol 77 (2) ◽  
pp. 315-323 ◽  
Author(s):  
MEHDI ALAEIYAN ◽  
MOHSEN GHASEMI
Keyword(s):  
Undirected Graph ◽  
Cubic Graphs ◽  
Transitive Graph ◽  
Symmetric Graphs ◽  
Vertex Transitive ◽  
Regular Line ◽  
Edge Transitive ◽  
Transitive Graphs

AbstractA simple undirected graph is said to be semisymmetric if it is regular and edge-transitive but not vertex-transitive. Let p be a prime. It was shown by Folkman [J. Folkman, ‘Regular line-symmetric graphs’, J. Combin. Theory3 (1967), 215–232] that a regular edge-transitive graph of order 2p or 2p2 is necessarily vertex-transitive. In this paper an extension of his result in the case of cubic graphs is given. It is proved that every cubic edge-transitive graph of order 8p2 is vertex-transitive.

scholarly journals k-Sums in Abelian Groups

2012 ◽  
Vol 21 (4) ◽  
pp. 582-596 ◽  
Author(s):  
BENJAMIN GIRARD ◽  
SIMON GRIFFITHS ◽  
YAHYA OULD HAMIDOUNE
Keyword(s):  
Abelian Group ◽  
Finite Subset ◽  
Complete Graph ◽  
Abelian Groups ◽  
Elementary Property ◽  
Finite Sets ◽  
Edge Colourings

Given a finite subset A of an abelian group G, we study the set k ∧ A of all sums of k distinct elements of A. In this paper, we prove that |k ∧ A| ≥ |A| for all k ∈ {2,. . .,|A| − 2}, unless k ∈ {2, |A| − 2} and A is a coset of an elementary 2-subgroup of G. Furthermore, we characterize those finite sets A ⊆ G for which |k ∧ A| = |A| for some k ∈ {2,. . .,|A| − 2}. This result answers a question of Diderrich. Our proof relies on an elementary property of proper edge-colourings of the complete graph.

scholarly journals Biased Positional Games and Small Hypergraphs with Large Covers

10.37236/794 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Michael Krivelevich ◽  
Tibor Szabó
Keyword(s):  
Complete Graph ◽  
Winning Strategy ◽  
Hamilton Cycle ◽  
Covering Number ◽  
New Approach ◽  
Positional Games

We prove that in the biased $(1:b)$ Hamiltonicity and $k$-connectivity Maker-Breaker games ($k>0$ is a constant), played on the edges of the complete graph $K_n$, Maker has a winning strategy for $b\le(\log 2-o(1))n/\log n$. Also, in the biased $(1:b)$ Avoider-Enforcer game played on $E(K_n)$, Enforcer can force Avoider to create a Hamilton cycle when $b\le (1-o(1))n/\log n$. These results are proved using a new approach, relying on the existence of hypergraphs with few edges and large covering number.

scholarly journals A new approach to complete graph

2017 ◽  
Vol 1 (5) ◽  
pp. 264-268
Author(s):  
Basheer Ahamed Mohideen
Keyword(s):  
Complete Graph ◽  
New Approach

The O–C diagrams of minor planets − a new approach to modelling the rotation

1999 ◽  
Vol 173 ◽  
pp. 185-188
Author(s):  
Gy. Szabó ◽  
K. Sárneczky ◽  
L.L. Kiss
Keyword(s):  
Error Analysis ◽  
Time Dependence ◽  
Theoretical Work ◽  
Minor Planet ◽  
Minor Planets ◽  
New Approach ◽  
Preliminary Results ◽  
Ccd Observations

AbstractA widely used tool in studying quasi-monoperiodic processes is the O–C diagram. This paper deals with the application of this diagram in minor planet studies. The main difference between our approach and the classical O–C diagram is that we transform the epoch (=time) dependence into the geocentric longitude domain. We outline a rotation modelling using this modified O–C and illustrate the abilities with detailed error analysis. The primary assumption, that the monotonity and the shape of this diagram is (almost) independent of the geometry of the asteroids is discussed and tested. The monotonity enables an unambiguous distinction between the prograde and retrograde rotation, thus the four-fold (or in some cases the two-fold) ambiguities can be avoided. This turned out to be the main advantage of the O–C examination. As an extension to the theoretical work, we present some preliminary results on 1727 Mette based on new CCD observations.

A New Approach to the Demonstration of Oxidase-Localization Using Tannic Acid Or Catechin

1973 ◽  
Vol 31 ◽  
pp. 698-699
Author(s):  
V. Mizuhira ◽  
Y. Futaesaku
Keyword(s):  
Cross Section ◽  
Tannic Acid ◽  
Elastic Fiber ◽  
The Other ◽  
New Approach ◽  
Tissue Block ◽  
Active Reaction ◽  
The Cross

Previously we reported that tannic acid is a very effective fixative for proteins including polypeptides. Especially, in the cross section of microtubules, thirteen submits in A-tubule and eleven in B-tubule could be observed very clearly. An elastic fiber could be demonstrated very clearly, as an electron opaque, homogeneous fiber. However, tannic acid did not penetrate into the deep portion of the tissue-block. So we tried Catechin. This shows almost the same chemical natures as that of proteins, as tannic acid. Moreover, we thought that catechin should have two active-reaction sites, one is phenol,and the other is catechole. Catechole site should react with osmium, to make Os- black. Phenol-site should react with peroxidase existing perhydroxide.

Processing Immunoperoxidase Labeled Cell Monolayers and Cryostat Sesctions For Electron Microscopy

1985 ◽  
Vol 43 ◽  
pp. 714-715
Author(s):  
K. Chien ◽  
R. Van de Velde ◽  
I.P. Shintaku ◽  
A.F. Sassoon
Keyword(s):  
Cell Monolayer ◽  
Cell Types ◽  
Surface Antigens ◽  
Immunoperoxidase Method ◽  
Reaction Step ◽  
Hot Plate ◽  
Air Drying ◽  
New Approach ◽  
Cell Monolayers ◽  
Glass Slides

Immunoelectron microscopy of neoplastic lymphoma cells is valuable for precise localization of surface antigens and identification of cell types. We have developed a new approach in which the immunohistochemical staining can be evaluated prior to embedding for EM and desired area subsequently selected for ultrathin sectioning.A freshly prepared lymphoma cell suspension is spun onto polylysine hydrobromide- coated glass slides by cytocentrifugation and immediately fixed without air drying in polylysine paraformaldehyde (PLP) fixative. After rinsing in PBS, slides are stained by a 3-step immunoperoxidase method. Cell monolayer is then fixed in buffered 3% glutaraldehyde prior to DAB reaction. After the DAB reaction step, wet monolayers can be examined under LM for presence of brown reaction product and selected monolayers then processed by routine methods for EM and embedded with the Chien Re-embedding Mold. After the polymerization, the epoxy blocks are easily separated from the glass slides by heatingon a 100°C hot plate for 20 seconds.

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