Page 320 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 320
GROUPS, GRAPHS AND NETWORKS (MS-75)
every connected symmetric Cayley graph of T of valency r is normal. Employing maximal
factorizations of finite almost simple groups, we work out a possible list of those exceptions for
T.
Symmetric cubic graphs with non-solvable automorphism groups
Jicheng Ma, ma_jicheng@hotmail.com
Chongqing University of Arts and Sciences, China
A cubic graph Γ is called G-symmetric if a group G of automorphisms of Γ acts transitively
on the arcs of Γ, and G-basic if it is G-symmetric and G has no non-trivial normal subgroups
with more than two orbits on the vertex set of Γ. We say the graph Γ is basic if it is G-basic
for all arc-transitive subgroups of Aut(Γ). In this talk, a characterization of basic symmetric
cubic graphs with non-solvable automorphism groups will be discussed. This is a joint work
with Jin-Xin Zhou.
Symmetric properties, reliabilities and Hamiltonian cycles of some
hypercube-like networks
Da Wei Yang, dwyang@bupt.edu.cn
Beijing University of Posts and Telecommunications, China
The class of hypercube-like networks was proposed by Vaidya et al. in 1993, which includes
numerous well-known topologies, such as hypercubes, locally twisted cubes, the spined cubes,
and crossed cubes. In this talk, I will present our recent works on symmetric properties, relia-
bilities, and Hamiltonian cycles of some hypercube-like networks.
Trivalent dihedrants and bi-dihedrants
Mimi Zhang, mmzhang@hebtu.edu.cn
Hebei Normal University, China
A Cayley (resp. bi-Cayley) graph on a dihedral group is called a dihedrant (resp. bi-dihedrant).
In 2000, a classification of trivalent arc-transitive dihedrants was given by Marušicˇ and Pisanski,
and several years later, trivalent non-arc-transitive dihedrants of order 4p or 8p (p a prime)
were classified by Feng et al. As a generalization of these results, our first result presents a
classification of trivalent non-arc-transitive dihedrants. Using this, a complete classification of
trivalent vertex-transitive non-Cayley bi-dihedrants is given. As a by-product, we generalize a
theorem in [The Electronic Journal of Combinatorics 19 (2012) #P53].
This is joint work with Jin-Xin Zhou.
318
every connected symmetric Cayley graph of T of valency r is normal. Employing maximal
factorizations of finite almost simple groups, we work out a possible list of those exceptions for
T.
Symmetric cubic graphs with non-solvable automorphism groups
Jicheng Ma, ma_jicheng@hotmail.com
Chongqing University of Arts and Sciences, China
A cubic graph Γ is called G-symmetric if a group G of automorphisms of Γ acts transitively
on the arcs of Γ, and G-basic if it is G-symmetric and G has no non-trivial normal subgroups
with more than two orbits on the vertex set of Γ. We say the graph Γ is basic if it is G-basic
for all arc-transitive subgroups of Aut(Γ). In this talk, a characterization of basic symmetric
cubic graphs with non-solvable automorphism groups will be discussed. This is a joint work
with Jin-Xin Zhou.
Symmetric properties, reliabilities and Hamiltonian cycles of some
hypercube-like networks
Da Wei Yang, dwyang@bupt.edu.cn
Beijing University of Posts and Telecommunications, China
The class of hypercube-like networks was proposed by Vaidya et al. in 1993, which includes
numerous well-known topologies, such as hypercubes, locally twisted cubes, the spined cubes,
and crossed cubes. In this talk, I will present our recent works on symmetric properties, relia-
bilities, and Hamiltonian cycles of some hypercube-like networks.
Trivalent dihedrants and bi-dihedrants
Mimi Zhang, mmzhang@hebtu.edu.cn
Hebei Normal University, China
A Cayley (resp. bi-Cayley) graph on a dihedral group is called a dihedrant (resp. bi-dihedrant).
In 2000, a classification of trivalent arc-transitive dihedrants was given by Marušicˇ and Pisanski,
and several years later, trivalent non-arc-transitive dihedrants of order 4p or 8p (p a prime)
were classified by Feng et al. As a generalization of these results, our first result presents a
classification of trivalent non-arc-transitive dihedrants. Using this, a complete classification of
trivalent vertex-transitive non-Cayley bi-dihedrants is given. As a by-product, we generalize a
theorem in [The Electronic Journal of Combinatorics 19 (2012) #P53].
This is joint work with Jin-Xin Zhou.
318
