A class of interconnection networks for efficient parallel MD simulations based on hamiltonian cubic symmetric graphs is presented. The cubic symmetric graphs have many desirable properties as ...interconnection networks since they have a low degree and are vertex- and edge-transitive. We present a method for scheduling collective communication routines that are used in parallel MD and are based on the property that the graphs in question have a Hamilton cycle, that is, a cycle going through all vertices of the graph. Analyzing these communication routines shows that hamiltonian cubic symmetric graphs of small diameter are good candidates for a topology that gives rise to an interconnection network with excellent properties, allowing faster communication and thus speeding up parallel MD simulation.
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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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
When dealing with symmetry properties of mathematical objects, one of the fundamental questions is to determine their full automorphism group. In this paper this question is considered in the context ...of even/odd permutations dichotomy. More precisely: when is it that the existence of automorphisms acting as even permutations on the vertex set of a graph, called even automorphisms, forces the existence of automorphisms that act as odd permutations, called odd automorphisms. As a first step towards resolving the above question, complete information on the existence of odd automorphisms in cubic symmetric graphs is given.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Two elements
g
,
h
of a permutation group
G
acting on a set
V
are said to be
intersecting
if
g
(
v
)
=
h
(
v
)
for some
v
∈
V
. More generally, a subset
F
of
G
is an
intersecting set
if every pair ...of elements of
F
is intersecting. The intersection density
ρ
(
G
)
of a transitive permutation group
G
is the maximum value of the quotient
|
F
|
/
|
G
v
|
where
F
runs over all intersecting sets in
G
and
G
v
is the stabilizer of
v
∈
V
. A vertex-transitive graph
X
is
intersection density stable
if any two transitive subgroups of
Aut
(
X
)
have the same intersection density. This paper studies the above concepts in the context of cubic symmetric graphs. While a 1-regular cubic symmetric graph is necessarily intersection density stable, the situation for 2-arc-regular cubic symmetric graphs is more complex. A necessary condition for a 2-arc-regular cubic symmetric graph admitting a 1-arc-regular subgroup of automorphisms to be intersection density stable is given, and an infinite family of such graphs is constructed.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
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