scholarly journals Edge-colourings of cubic graphs admitting a solvable vertex-transitive group of automorphisms

2004 ◽  
Vol 91 (2) ◽  
pp. 289-300 ◽  
Author(s):  
Primož Potočnik
Keyword(s):  
Transitive Group ◽  
Cubic Graphs ◽  
Group Of Automorphisms ◽  
Vertex Transitive ◽  
Edge Colourings

scholarly journals Semiregular Automorphisms of Cubic Vertex-Transitive Graphs and the Abelian Normal Quotient Method

10.37236/4842 ◽  
2015 ◽  
Vol 22 (3) ◽  
Author(s):  
Joy Morris ◽  
Pablo Spiga ◽  
Gabriel Verret
Keyword(s):  
Transitive Group ◽  
Cubic Graphs ◽  
Cubic Graph ◽  
Maximum Order ◽  
Abelian Normal Subgroup ◽  
Group Of Automorphisms ◽  
Normal Quotient ◽  
Vertex Transitive ◽  
Vertex Transitive Graphs ◽  
Transitive Graphs

We characterise connected cubic graphs admitting a vertex-transitive group of automorphisms with an abelian normal subgroup that is not semiregular. We illustrate the utility of this result by using it to prove that the order of a semiregular subgroup of maximum order in a vertex-transitive group of automorphisms of a connected cubic graph grows with the order of the graph.

ON ISOMORPHISMS OF VERTEX-TRANSITIVE CUBIC GRAPHS

2015 ◽  
Vol 99 (3) ◽  
pp. 341-349
Author(s):  
JING CHEN ◽  
CAI HENG LI ◽  
WEI JUN LIU
Keyword(s):  
Simple Group ◽  
Isomorphism Problem ◽  
Cubic Graphs ◽  
Group Of Automorphisms ◽  
Vertex Transitive

We study the isomorphism problem of vertex-transitive cubic graphs which have a transitive simple group of automorphisms.

scholarly journals Finite Edge-Transitive Oriented Graphs of Valency Four: a Global Approach

10.37236/4779 ◽  
2016 ◽  
Vol 23 (1) ◽  
Author(s):  
Jehan A. Al-bar ◽  
Ahmad N. Al-kenani ◽  
Najat M. Muthana ◽  
Cheryl E. Praeger ◽  
Pablo Spiga
Keyword(s):  
Transitive Group ◽  
Open Problems ◽  
Oriented Graphs ◽  
Group Of Automorphisms ◽  
Normal Quotient ◽  
Normal Cover ◽  
Vertex Transitive ◽  
Edge Transitive ◽  
Basic Graph ◽  
New Framework

We develop a new framework for analysing finite connected, oriented graphs of valency four, which admit a vertex-transitive and edge-transitive group of automorphisms preserving the edge orientation. We identify a sub-family of `basic' graphs such that each graph of this type is a normal cover of at least one basic graph. The basic graphs either admit an edge-transitive group of automorphisms that is quasiprimitive or biquasiprimitive on vertices, or admit an (oriented or unoriented) cycle as a normal quotient. We anticipate that each of these additional properties will facilitate effective further analysis, and we demonstrate that this is so for the quasiprimitive basic graphs. Here we obtain strong restrictions on the group involved, and construct several infinite families of such graphs which, to our knowledge, are different from any recorded in the literature so far. Several open problems are posed in the paper.

scholarly journals Characterisation Results for Steiner Triple Systems and Their Application to Edge-Colourings of Cubic Graphs

2010 ◽  
Vol 62 (2) ◽  
pp. 355-381 ◽  
Author(s):  
Daniel Král’ ◽  
Edita Máčajov´ ◽  
Attila Pór ◽  
Jean-Sébastien Sereni
Keyword(s):  
Triple System ◽  
Steiner Triple System ◽  
Cubic Graphs ◽  
Steiner Triple Systems ◽  
Cubic Graph ◽  
Triple Systems ◽  
Forbidden Configurations ◽  
Edge Colourings

AbstractIt is known that a Steiner triple system is projective if and only if it does not contain the four-triple configuration C14. We find three configurations such that a Steiner triple system is affine if and only if it does not contain one of these configurations. Similarly, we characterise Hall triple systems using two forbidden configurations.Our characterisations have several interesting corollaries in the area of edge-colourings of graphs. A cubic graph G is S-edge-colourable for a Steiner triple system S if its edges can be coloured with points of S in such a way that the points assigned to three edges sharing a vertex form a triple in S. Among others, we show that all cubic graphs are S-edge-colourable for every non-projective nonaffine point-transitive Steiner triple system S.

scholarly journals Cubic Non-Cayley Vertex-Transitive Bi-Cayley Graphs over a Regular $p$-Group

10.37236/3915 ◽  
2016 ◽  
Vol 23 (3) ◽  
Author(s):  
Jin-Xin Zhou ◽  
Yan-Quan Feng
Keyword(s):  
Cayley Graph ◽  
Cayley Graphs ◽  
Equal Size ◽  
Group Of Automorphisms ◽  
Vertex Transitive ◽  
Vertex Transitive Graphs ◽  
Transitive Graphs

A bi-Cayley graph is a graph which admits a semiregular group of automorphisms with two orbits of equal size. In this paper, we give a characterization of cubic non-Cayley vertex-transitive bi-Cayley graphs over a regular $p$-group, where $p>5$ is an odd prime. As an application, a classification of cubic non-Cayley vertex-transitive graphs of order $2p^3$ is given for each prime $p$.

scholarly journals Classification of 4- and 5-arc-transitive cubic graphs of small girth: corrigendum

1992 ◽  
Vol 52 (3) ◽  
pp. 419-420
Author(s):  
Margaret J. Morton
Keyword(s):  
Cubic Graphs ◽  
Regular Group ◽  
Group Of Automorphisms ◽  
Transitive Graphs

The purpose of this brief note is to point out an omission, at the top of page 145, in my paper [1]. Richard Weiss has kindly pointed out that there exist 5-arc-transitive graphs with no 4-arc regular group of automorphisms.

Vertex-Transitive Cubic Graphs of Square-Free Order

2013 ◽  
Vol 75 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Cai Heng Li ◽  
Zai Ping Lu ◽  
Gai Xia Wang
Keyword(s):  
Cubic Graphs ◽  
Vertex Transitive ◽  
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