Pentavalent Symmetric Graphs of Order Twice a Prime Square

2015 ◽  
Vol 22 (03) ◽  
pp. 383-394 ◽  
Author(s):  
Jiangmin Pan ◽  
Zhe Liu ◽  
Xiaofen Yu

A classification of pentavalent symmetric graphs of order twice a prime square is given. It is proved that such a graph is a coset graph of ℤ3. A 6 (non-split extension), or a bi-coset graph of an extra-special group of order 125, or the standard double cover of a specific abelian Cayley digraph of order a prime square.

2011 ◽  
Vol 121 (3) ◽  
pp. 249-257
Author(s):  
MEHDI ALAEIYAN ◽  
B N ONAGH ◽  
M K HOSSEINIPOOR
Keyword(s):  

2014 ◽  
Vol 90 (3) ◽  
pp. 353-362 ◽  
Author(s):  
BO LING ◽  
CI XUAN WU ◽  
BEN GONG LOU

AbstractA complete classification is given of pentavalent symmetric graphs of order$30p$, where$p\ge 5$is a prime. It is proved that such a graph${\Gamma }$exists if and only if$p=13$and, up to isomorphism, there is only one such graph. Furthermore,${\Gamma }$is isomorphic to$\mathcal{C}_{390}$, a coset graph of PSL(2, 25) with${\sf Aut}\, {\Gamma }=\mbox{PSL(2, 25)}$, and${\Gamma }$is 2-regular. The classification involves a new 2-regular pentavalent graph construction with square-free order.


2013 ◽  
Vol 38 (3) ◽  
pp. 745-765 ◽  
Author(s):  
Massimo Giulietti ◽  
Stefano Marcugini ◽  
Fernanda Pambianco ◽  
Sanming Zhou
Keyword(s):  

1993 ◽  
Vol 58 (2) ◽  
pp. 197-216 ◽  
Author(s):  
R.J. Wang ◽  
M.Y. Xu
Keyword(s):  

10.37236/4035 ◽  
2014 ◽  
Vol 21 (3) ◽  
Author(s):  
Jicheng Ma

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.


10.12737/5276 ◽  
2014 ◽  
Vol 2 (8) ◽  
pp. 48-56
Author(s):  
Елена Орлова ◽  
Elena Orlova

The purpose of this article is to describe the legal relations in the field of employment and labor law relations. It is of immediate interest, because it is one of the important legal relations issues in jurisprudence. The article deals with the legal relations in the field of employment, which is of great scientific and practical importance, as it is implemented in legal relations subjective rights and duties of citizens in the field of employment. The analysis of the different viewpoints of scientists who studied the legal relations in the field of employment provides an opportunity to research the legal relations issues in the field of employment. The analysis of relations in the field of employment as “derivative from labor”, “related to labor”, “closely related to labor”, “indissolubly related to labor”, “adjoining to labor”, “elective satellites of labor” allows to research co-relation issues of the legal relations in the field of employment and labor law relation. The author defines a special group of the legal relations in the field of employment with certain characteristics and features. As a result of research all legal relations types of employment are presented and the classification of legal relations types by subject matter is carried out.


Author(s):  
Viktoria Viktorovna Yatsenko ◽  
Sergey Grigorievich Falco

The article describes the use of the competence approach in management practice, its connection with the acceleration of innovation processes, complexity of the applied technologies, flexibility in a dynamic external environment, when not only the availability of resources becomes important, but also the possibility of using them to ensure the sustainability and competitiveness of the organization. The analysis proves the complexity, multiplicity and interdisciplinarity of the concepts associated with the competence approach and classification of competencies, as well as with the absence of industry specificity in the construction of a typology of competencies. The high-tech products production requires going beyond the enterprise, since it is necessary to combine the efforts of several teams and even organizations to create complex innovative products. For the development of high-tech solutions, the search and integration of both internal and external capabilities becomes necessary. The high-tech innovative potential enterprises are based on the most sophisticated equipment and high technologies, highly skilled labor resources. Therefore, the task of forming and developing staff competencies at high-tech enterprises is becoming urgent. There have been listed consistent tendencies of using the concept of “competency”, pointed out the key features of competencies: flexibility and changeability, orientation toward executing functional (professional) tasks, dependency on a person’s motivations and values. There are discussed the traditional approaches to the typology of staff competencies. The architecture of competencies proposes taking into account the requirements for high-tech enterprises staff knowledge, skills and abilities. The rationale for identifying a special group of system competencies is given.


2019 ◽  
Vol 7 (5) ◽  
Author(s):  
Yuji Tachikawa ◽  
Kazuya Yonekura

Orientifold pp-planes with p\le 4p≤4 have fractional Dpp-charges, and therefore appear inconsistent with Dirac quantization with respect to D(6{-}p)(6−p)-branes. We explain in detail how this issue is resolved by taking into account the anomaly of the worldvolume fermions using the \etaη invariants. We also point out relationships to the classification of interacting fermionic symmetry protected topological phases. In an appendix, we point out that the duality group of type IIB string theory is the  pin^++ version of the double cover of GL(2,Z).


10.37236/720 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Song-Tao Guo ◽  
Jin-Xin Zhou ◽  
Yan-Quan Feng

A graph is said to be symmetric if its automorphism group acts transitively on its arcs. In this paper, a complete classification of connected pentavalent symmetric graphs of order $12p$ is given for each prime $p$. As a result, a connected pentavalent symmetric graph of order $12p$ exists if and only if $p=2$, $3$, $5$ or $11$, and up to isomorphism, there are only nine such graphs: one for each $p=2$, $3$ and $5$, and six for $p=11$.


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