A graph is called half-arc-transitive if its full automorphism group acts transitively on vertices and edges, but not on arcs. In this paper, we classify hexavalent half-arc-transitive graphs of ...order 9p for each prime p. As a result, there are four infinite families of such graphs: three defined on Zp⋊Z27 with 27|(p−1); one defined on Z3p⋊Z9 with 9|(p−1).
A family of tetravalent half-arc-transitive graphs Biswas, Sucharita; Das, Angsuman
Proceedings of the Indian Academy of Sciences. Mathematical sciences,
10/2021, Volume:
131, Issue:
2
Journal Article
Peer reviewed
Alspach
et al
. (
J. Austral. Math. Soc
.
56(3)
(1994) 391–402) constructed an infinite family of tetravalent graphs
M
(
a
;
m
,
n
) and proved that if
n
≥
9
be odd and
a
3
≡
1
(
mod
n
)
, then
M
(
...a
; 3,
n
) is half-arc-transitive. In this paper, we show that if
a
3
≡
1
(
mod
n
)
, then
M
(
a
; 3,
n
) is an infinite family of tetravalent half-arc-transitive Cayley graphs for all integers
n
except 7 and 14.
A graph is
half-arc-transitive
if its automorphism group acts transitively on its vertex set, edge set, but not arc set. Let
p
be a prime. It is known that there exist no tetravalent ...half-arc-transitive graphs of order
p
or 2
p
. Feng et al. (J Algebraic Combin 26:431–451,
2007
) gave the classification of tetravalent half-arc-transitive graphs of order 4
p
. In this paper, a classification is given of all tetravalent half-arc-transitive graphs of order 8
p
.
A graph is half-arc-transitive if its automorphism group acts transitively on its vertex set, edge set, but not arc set. Let n be a product of three primes. The problem on the classification of the ...tetravalent half-arc-transitive graphs of order n has been considered by Xu (1992), Feng et al. (2007) and Wang and Feng (2010), and it was solved for the cases where n is a prime cube or twice a product of two primes. In this paper, we solve this problem for the remaining cases. In particular, there exist some families of these graphs which have a solvable automorphism group but are not metacirculants.
A graph is
half-arc-transitive
if its automorphism group acts transitively on vertices and edges, but not on arcs. Let
p
be a prime. A graph is called a
p
-graph
if it is a Cayley graph of order a ...power of
p
. In this paper, a characterization is given of tetravalent edge-transitive
p
-graphs with
p
an odd prime. This is then applied to construct infinitely many connected tetravalent half-arc-transitive non-normal
p
-graphs with
p
an odd prime, and to initiate an investigation of tetravalent half-arc-transitive non-metacirculant
p
-graphs with
p
an odd prime. As by-products, two problems reported in the literature are answered.
A graph is half-arc-transitive if its automorphism group acts transitively on its vertex set, edge set, but not arc set. In this paper, we show that there is no tetravalent half-arc-transitive graph ...of order
2
p
2
.
A graph is
half-arc-transitive
if its automorphism group acts transitively on its vertex set, edge set, but not arc set. Let
p
and
q
be primes. It is known that no tetravalent half-arc-transitive ...graphs of order 2
p
2
exist and a tetravalent half-arc-transitive graph of order 4
p
must be non-Cayley; such a non-Cayley graph exists if and only if
p
−1 is divisible by 8 and it is unique for a given order. Based on the constructions of tetravalent half-arc-transitive graphs given by Marušič (J. Comb. Theory B 73:41–76,
1998
), in this paper the connected tetravalent half-arc-transitive graphs of order 2
pq
are classified for distinct odd primes
p
and
q
.
A graph is half-arc-transitive if its automorphism group acts transitively on vertices and edges, but not on arcs. In this paper, a new infinite family of tetravalent half-arc-transitive graphs with ...girth 4 is constructed, each of which has order
16
m
such that
m
>
1
is a divisor of
2
t
2
+
2
t
+
1
for a positive integer
t and is tightly attached with attachment number
4
m
. The smallest graph in the family has order 80.
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