Page 319 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 319
GROUPS, GRAPHS AND NETWORKS (MS-75)
Groups and skew morphisms
Kan Hu, hukan@zjou.edu.cn
Zhejiang Ocean University, China
In this talk I will give a survey of the theory of skew morphisms, and post several unsolved
problems related to symmetric embeddings of graphs into orientable closed surfaces.
The s-geodesic-transitivity of graphs
Wei Jin, jinweipei82@163.com
Central South University, China
Coauthors: Alice Devillers, Caiheng Li, Cheryl Praeger
In a finite graph Γ, a geodesic from a vertex u to a vertex v is one of the shortest paths from
u to v, and this geodesic is called an i-geodesic if the distance between u and v is i. The
graph Γ is said to be s-geodesic-transitive if the graph automorphism group is transitive on the
set of s-geodesics. In this talk, I will compare the s-geodesic-transitivity of graphs with other
two well-known transitive properties, namely s-arc-transitivity and s-distance-transitivity, and
determine the local structure of 2-geodesic-transitive graphs, and also give some results about
the family of locally disconnected 2-geodesic-transitive but not 2-arc-transitive graphs.
Skew morphisms of finite groups with applications
István Kovács, istvan.kovacs@upr.si
University of Primorska, Slovenia
A skew morphism of a finite group G is a bijection ϕ : G → G fixing the identity element of G
and having the property that ϕ(xy) = ϕ(x)ϕπ(x)(y) for all x, y ∈ G, where π(x) depends only
on x. Skew morphisms generalise group automorphisms and were introduced in the context
of topological graph theory by Jajcay and Širánˇ (2002). In this talk, I review some recent
results on skew morphisms and also mention some applications. These applications include a
connection with the complementary product of a group with a cyclic group, the classification
of regular Cayley maps for dihedral groups, and a connection with block transpositions (well-
known sorting operations with relevant applications in Bioinformatics).
Symmetric graphs of prime valency
Zai Ping Lu, lu@nankai.edu.cn
Nankai University, China
A graph Γ = (V, E) is called a Cayley graph of some group T if the automorphism group
Aut(Γ) contains a subgroup T which acts on regularly on V . If the subgroup T is normal
in Aut(Γ) then Γ is called a normal Cayley graph of T . Let r be an odd prime. Fang et al.
[On locally primitive Cayley graphs of finite simple groups, J. Combin. Theory Ser. A 118
(2011), 1039-1051] proved that, with a finite number of exceptions for finite simple group T ,
317
Groups and skew morphisms
Kan Hu, hukan@zjou.edu.cn
Zhejiang Ocean University, China
In this talk I will give a survey of the theory of skew morphisms, and post several unsolved
problems related to symmetric embeddings of graphs into orientable closed surfaces.
The s-geodesic-transitivity of graphs
Wei Jin, jinweipei82@163.com
Central South University, China
Coauthors: Alice Devillers, Caiheng Li, Cheryl Praeger
In a finite graph Γ, a geodesic from a vertex u to a vertex v is one of the shortest paths from
u to v, and this geodesic is called an i-geodesic if the distance between u and v is i. The
graph Γ is said to be s-geodesic-transitive if the graph automorphism group is transitive on the
set of s-geodesics. In this talk, I will compare the s-geodesic-transitivity of graphs with other
two well-known transitive properties, namely s-arc-transitivity and s-distance-transitivity, and
determine the local structure of 2-geodesic-transitive graphs, and also give some results about
the family of locally disconnected 2-geodesic-transitive but not 2-arc-transitive graphs.
Skew morphisms of finite groups with applications
István Kovács, istvan.kovacs@upr.si
University of Primorska, Slovenia
A skew morphism of a finite group G is a bijection ϕ : G → G fixing the identity element of G
and having the property that ϕ(xy) = ϕ(x)ϕπ(x)(y) for all x, y ∈ G, where π(x) depends only
on x. Skew morphisms generalise group automorphisms and were introduced in the context
of topological graph theory by Jajcay and Širánˇ (2002). In this talk, I review some recent
results on skew morphisms and also mention some applications. These applications include a
connection with the complementary product of a group with a cyclic group, the classification
of regular Cayley maps for dihedral groups, and a connection with block transpositions (well-
known sorting operations with relevant applications in Bioinformatics).
Symmetric graphs of prime valency
Zai Ping Lu, lu@nankai.edu.cn
Nankai University, China
A graph Γ = (V, E) is called a Cayley graph of some group T if the automorphism group
Aut(Γ) contains a subgroup T which acts on regularly on V . If the subgroup T is normal
in Aut(Γ) then Γ is called a normal Cayley graph of T . Let r be an odd prime. Fang et al.
[On locally primitive Cayley graphs of finite simple groups, J. Combin. Theory Ser. A 118
(2011), 1039-1051] proved that, with a finite number of exceptions for finite simple group T ,
317
