A classification of cubic symmetric graphs of order 16p 2

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

scholarly journals Unitary graphs and classification of a family of symmetric graphs with complete quotients

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

scholarly journals A Classification of Symmetric Graphs of Order 3p

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

Pentavalent Symmetric Graphs of Order Twice a Prime Square

2015 ◽  
Vol 22 (03) ◽  
pp. 383-394 ◽  
Author(s):  
Jiangmin Pan ◽  
Zhe Liu ◽  
Xiaofen Yu
Keyword(s):  
Double Cover ◽  
Split Extension ◽  
Special Group ◽  
Cayley Digraph ◽  
Symmetric Graphs ◽  
Coset Graph

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.

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.

scholarly journals Pentavalent Symmetric Graphs of Order $12p$

10.37236/720 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Song-Tao Guo ◽  
Jin-Xin Zhou ◽  
Yan-Quan Feng
Keyword(s):  
Automorphism Group ◽  
Complete Classification ◽  
Symmetric Graph ◽  
Symmetric Graphs

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 $p=11$.

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 On the Crossing Numbers of the Join Products of Six Graphs of Order Six with Paths and Cycles

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2441
Author(s):  
Michal Staš
Keyword(s):  
Lower Bounds ◽  
Crossing Number ◽  
Crossing Numbers ◽  
Symmetric Graphs ◽  
The Family ◽  
Minimum Number ◽  
The Common ◽  
First Time ◽  
Edge Crossings

The crossing number of a graph G is the minimum number of edge crossings over all drawings of G in the plane. The main purpose of this paper is to determine the crossing numbers of the join products of six symmetric graphs on six vertices with paths and cycles on n vertices. The idea of configurations is generalized for the first time onto the family of subgraphs whose edges cross the edges of the considered graph at most once, and their lower bounds of necessary numbers of crossings are presented in the common symmetric table. Some proofs of the join products with cycles are done with the help of several well-known auxiliary statements, the idea of which is extended by a suitable classification of subgraphs that do not cross the edges of the examined graphs.

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