Three-arc graphs: characterization and domination

An arc of a graph is an oriented edge and a 3-arc is a 4-tuple $(v,u,x,y)$ of vertices such that both $(v,u,x)$ and $(u,x,y)$ are paths of length two. The 3-arc graph of a graph $G$ is defined to have vertices the arcs of $G$ such that two arcs $uv, xy$ are adjacent if and only if $(v,u,x,y)$ is a 3-arc of $G$. 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 $G$ in terms that of $G$

Hadwiger's conjecture for 3-arc graphs

The 3-arc graph of a digraph $D$ is defined to have vertices the arcs of $D$ such that two arcs $uv, xy$ are adjacent if and only if $uv$ and $xy$ are distinct arcs of $D$ with $v\ne x$, $y\ne u$ and $u,x$ adjacent. We prove that Hadwiger's conjecture holds for 3-arc graphs

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

Symmetric graphs with 2-arc transitive quotients

A graph \Ga is $G$-symmetric if \Ga admits $G$ 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 $G$ is imprimitive on V(\Ga), namely when V(\Ga) admits a nontrivial $G$-invariant partition \BB, the quotient graph \Ga_{\BB} of \Ga with respect to \BB is always $G$-symmetric and sometimes even $(G, 2)$-arc transitive. (A $G$-symmetric graph is $(G, 2)$-arc transitive if $G$ is transitive on the set of oriented paths of length two.) In this paper we obtain necessary conditions for \Ga_{\BB} to be $(G, 2)$-arc transitive (regardless of whether \Ga is $(G, 2)$-arc transitive) in the case when $v-k$ is an odd prime $p$, where $v$ is the block size of \BB and $k$ is the number of vertices in a block having neighbours in a fixed adjacent block. These conditions are given in terms of $v, k$ 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 $p=3$ or $5$ then these necessary conditions are essentially sufficient for \Ga_{\BB} to be $(G, 2)$-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"

Hamiltonicity of 3-arc graphs

An arc of a graph is an oriented edge and a 3-arc is a 4-tuple $(v,u,x,y)$ of vertices such that both $(v,u,x)$ and $(u,x,y)$ are paths of length two. The 3-arc graph of a graph $G$ is defined to have vertices the arcs of $G$ such that two arcs $uv, xy$ are adjacent if and only if $(v,u,x,y)$ is a 3-arc of $G$. In this paper we prove that any connected 3-arc graph is Hamiltonian, and all iterative 3-arc graphs of any connected graph of minimum degree at least three are Hamiltonian. As a consequence we obtain that if a vertex-transitive graph is isomorphic to the 3-arc graph of a connected arc-transitive graph of degree at least three, then it is Hamiltonian. This confirms the well known conjecture, that all vertex-transitive graphs with finitely many exceptions are Hamiltonian, for a large family of vertex-transitive graphs. We also prove that if a graph with at least four vertices is Hamilton-connected, then so are its iterative 3-arc graphs.Comment: in press Graphs and Combinatorics, 201