A graph is
s-regular if its automorphism group acts regularly on the set of its
s-arcs. In this paper, the
s-regular elementary abelian coverings of the complete bipartite graph
K
3
,
3
and the
...s-regular cyclic or elementary abelian coverings of the complete graph
K
4
for each
s
⩾
1
are classified when the fibre-preserving automorphism groups act arc-transitively. A new infinite family of cubic 1-regular graphs with girth 12 is found, in which the smallest one has order 2058. As an interesting application, a complete list of pairwise non-isomorphic
s-regular cubic graphs of order 4
p, 6
p,
4
p
2
or
6
p
2
is given for each
s
⩾
1
and each prime
p.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
A graph is
s
-
regular if its automorphism group acts regularly on the set of its
s
-arcs. In this paper, we classify the cubic
s
-regular cubic graphs of order
14
p
for each
s
≥
1
and each prime
p
.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
An 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.
A graph is
s-
regular if its automorphism group acts regularly on the set of
s-arcs. An infinite family of cubic 1-regular graphs was constructed in European J. Combin. 23 (2002) 559, as cyclic ...coverings of the three-dimensional hypercube
Q
3. In this paper, we classify the
s-regular cyclic coverings of
Q
3 for each
s≥1, whose fibre-preserving automorphism subgroups act arc-transitively. As a result, a new infinite family of cubic 1-regular graphs is constructed.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
A graph is s-regular if its automorphism group acts regularly on the set of its s-arcs.An infinite family of cubic 1-regular graphs was constructed in 7 as cyclic coverings of the three-dimensional ...Hypercube, and a classification of all s-regular cyclic coverings of the complete bipartite graph of order 6 was given in 8 for each s≥1, whose fibrepreserving automorphism subgroups act arc-transitively. In this paper, the authors classify all s-regular dihedral coverings of the complete graph of order 4 for each s ≥ 1,whose fibre-preserving automorphism subgroups act arc-transitively. As a result, a new infinite family of cubic 1-regular graphs is constructed.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
A cycle in a graph is consistent if the automorphism group of the graph admits a one‐step rotation of this cycle. A thorough description of consistent cycles of arc‐transitive subgroups in the full ...automorphism groups of finite cubic symmetric graphs is given.
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BFBNIB, FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SBCE, SBMB, UL, UM, UPUK
An 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. In this paper, we ...classify all connected cubic symmetric graphs of order 52p2 for each prime p.
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DOBA, IZUM, KILJ, NUK, ODKLJ, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
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