On the Spectrum of Wenger Graphs

Let $q=p^e$, where $p$ is a prime and $e\geq 1$ is an integer. For $m\geq 1$, let $P$ and $L$ be two copies of the $(m+1)$-dimensional vector spaces over the finite field $\mathbb{F}_q$. Consider the bipartite graph $W_m(q)$ with partite sets $P$ and $L$ defined as follows: a point $(p)=(p_1,p_2,\ldots,p_{m+1})\in P$ is adjacent to a line $[l]=[l_1,l_2,\ldots,l_{m+1}]\in L$ if and only if the following $m$ equalities hold: $l_{i+1} + p_{i+1}=l_{i}p_1$ for $i=1,\ldots, m$. We call the graphs $W_m(q)$ Wenger graphs. In this paper, we determine all distinct eigenvalues of the adjacency matrix of $W_m(q)$ and their multiplicities. We also survey results on Wenger graphs.Comment: 9 pages; accepted for publication to J. Combin. Theory, Series

Disconnecting strongly regular graphs

In this paper, we show that the minimum number of vertices whose removal disconnects a connected strongly regular graph into non-singleton components, equals the size of the neighborhood of an edge for many graphs. These include blocks graphs of Steiner $2$-designs, many Latin square graphs and strongly regular graphs whose intersection parameters are at most a quarter of their valency

Phonon nanocapacitor for storage and lasing of terahertz lattice waves

We introduce a novel ultra-compact nanocapacitor of coherent phonons formed by high-finesse interference mirrors based on atomic-scale semiconductor metamaterials. Our molecular dynamics simulations show that the nanocapacitor stores THz monochromatic lattice waves, which can be used for phonon lasing - the emission of coherent phonons. Either one- or two-color phonon lasing can be realized depending on the geometry of the nanodevice. The two color regimes of the capacitor originates from the distinct transmittance dependance on the phonon wave packet incident angle for the two phonon polarizations at their respective resonances. Phonon nanocapacitor can be charged by cooling the sample equilibrated at room temperature or by the pump-probe technique. The nanocapacitor can be discharged by applying tunable reversible strain, resulting in the emission of coherent THz acoustic beams.Comment: 12 pages, 5 figure

Solving the TTC 2011 Compiler Optimization Case with QVTR-XSLT

In this short paper we present our solution for the Compiler Optimization case study of the Transformation Tool Contest (TTC) 2011 using the QVTR-XSLT tool. The tool supports editing and execution of the graphical notation of QVT Relations languageComment: In Proceedings TTC 2011, arXiv:1111.440