175 research outputs found
Three-arc graphs: characterization and domination
An arc of a graph is an oriented edge and a 3-arc is a 4-tuple of
vertices such that both and are paths of length two. The
3-arc graph of a graph is defined to have vertices the arcs of such
that two arcs are adjacent if and only if is a 3-arc of
. In this paper we give a characterization of 3-arc graphs and obtain sharp
upper bounds on the domination number of the 3-arc graph of a graph in
terms that of
Hadwiger's conjecture for 3-arc graphs
The 3-arc graph of a digraph is defined to have vertices the arcs of
such that two arcs are adjacent if and only if and are
distinct arcs of with , and adjacent.
We prove that Hadwiger's conjecture holds for 3-arc graphs
Symmetric graphs with 2-arc transitive quotients
A graph \Ga is -symmetric if \Ga admits as a group of
automorphisms acting transitively on the set of vertices and the set of arcs of
\Ga, where an arc is an ordered pair of adjacent vertices. In the case when
is imprimitive on V(\Ga), namely when V(\Ga) admits a nontrivial
-invariant partition \BB, the quotient graph \Ga_{\BB} of \Ga with
respect to \BB is always -symmetric and sometimes even -arc
transitive. (A -symmetric graph is -arc transitive if is
transitive on the set of oriented paths of length two.) In this paper we obtain
necessary conditions for \Ga_{\BB} to be -arc transitive (regardless
of whether \Ga is -arc transitive) in the case when is an odd
prime , where is the block size of \BB and is the number of
vertices in a block having neighbours in a fixed adjacent block. These
conditions are given in terms of and two other parameters with respect
to (\Ga, \BB) together with a certain 2-point transitive block design induced
by (\Ga, \BB). We prove further that if or then these necessary
conditions are essentially sufficient for \Ga_{\BB} to be -arc
transitive.Comment: To appear in Journal of the Australian Mathematical Society. (The
previous title of this paper was "Finite symmetric graphs with two-arc
transitive quotients III"
Effects of practical impairments on cooperative distributed antennas combined with fractional frequency reuse
Cooperative Multiple Point (CoMP) transmission aided Distributed Antenna Systems (DAS) are proposed for increasing the received Signal-to-Interference-plus-Noise-Ratio (SINR) in the cell-edge area of a cellular system employing Fractional Frequency Reuse (FFR) in the presence of realistic imperfect Channel State Information (CSI) as well as synchronisation errors between the transmitters and the receivers. Our simulation results demonstrate that the CoMP aided DAS scenario is capable of increasing the attainable SINR by up to 3dB in the presence of a wide range of realistic imperfections
Characterization of the aggregation-induced enhanced emission of N,N'-bis(4-methoxysalicylide)benzene-1,4-diamine
© 2015 Springer Science+Business Media New York. N,N′-bis(4-methoxysalicylide)benzene-1,4-diamine (S1) was synthesized from 4-methoxysalicylaldehyde and p-phenylenediamine and it was found to exhibit interesting aggregation-induced emission enhancement (AIEE) characteristics. In aprotic solvent, S1 displayed very weak fluorescence, whilst strong emission was observed when in protic solvent. The morphology characteristics and luminescent properties of S1 were determined from the fluorescence and UV absorption spectra, SEM, fluorescence microscope and grading analysis. Analysis of the single crystal diffraction data infers that the intramolecular hydrogen bonding constitutes to a coplanar structure and orderly packing in aggregated state, which in turn hinders intramolecular C-N single bond rotation. Given that the three benzene rings formed a large plane conjugated structure, the fluorescence emission was significantly enhanced. The absolute fluorescence quantum yield and fluorescence lifetime also showed that radiation transition was effectively enhanced in the aggregated state. Moreover, the AIEE behavior of S1 suggests there is a potential application in the fluorescence sensing of some volatile organic solvents
The exact domination number of the generalized Petersen graphs
AbstractLet G=(V,E) be a graph. A subset S⊆V is a dominating set of G, if every vertex u∈V−S is dominated by some vertex v∈S. The domination number, denoted by γ(G), is the minimum cardinality of a dominating set. For the generalized Petersen graph G(n), Behzad et al. [A. Behzad, M. Behzad, C.E. Praeger, On the domination number of the generalized Petersen graphs, Discrete Mathematics 308 (2008) 603–610] proved that γ(G(n))≤⌈3n5⌉ and conjectured that the upper bound ⌈3n5⌉ is the exact domination number. In this paper we prove this conjecture
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