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The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform

Edo Waks - One of the best experts on this subject based on the ideXlab platform.

Ranojoy Bose - One of the best experts on this subject based on the ideXlab platform.

Satyabrata Paul - One of the best experts on this subject based on the ideXlab platform.

  • L(0, 1)-Labelling of Trapezoid Graphs
    International Journal of Applied and Computational Mathematics, 2017
    Co-Authors: Satyabrata Paul
    Abstract:

    L (0, 1)-labelling of a graph $$G=(V,E)$$ G = ( V , E ) is a function f from the vertex set V ( G ) to the set of non-negative integers such that adjacent vertices get number zero apart, and vertices at distance two get distinct numbers. The L (0, 1)-labelling number denoted by $$\lambda _{0,1}(G)$$ λ 0 , 1 ( G ) of G is the minimum range of labels over all such labelling. In this article, it is shown that, for a trapezoid graph G with maximum vertex degree $$\Delta $$ Δ , the upper bound of $$\lambda _{0,1}(G)$$ λ 0 , 1 ( G ) is $$\Delta -1$$ Δ - 1 .

  • L(0,1)-labelling of Permutation Graphs
    Journal of Mathematical Modelling and Algorithms in Operations Research, 2015
    Co-Authors: Satyabrata Paul
    Abstract:

    L (0,1)-labelling of a graph G =( V , E ) is a function f from the vertex set V ( G ) to the set of non-negative integers such that adjacent vertices get number zero apart, and vertices at distance two get distinct numbers. The goal of L (0,1)-labelling problem is to produce a legal labelling that minimize the largest label used. In this article, it is shown that, for a permutation graph G with maximum vertex degree Δ, the upper bound of λ _0,1( G ) is Δ−1. Finally, we prove that the result is exact for bipartite permutation graph.

  • L(2,1)-labeling of interval graphs
    Journal of Applied Mathematics and Computing, 2015
    Co-Authors: Satyabrata Paul
    Abstract:

    An $$L(2,1)$$ L ( 2 , 1 ) -labeling of a graph $$G=(V,E)$$ G = ( V , E ) is a function $$f$$ f from the vertex set $$V(G)$$ V ( G ) to the set of non-negative integers such that adjacent vertices get numbers at least two apart, and vertices at distance two get distinct numbers. The $$L(2,1)$$ L ( 2 , 1 ) -labeling number denoted by $$\lambda _{2,1}(G)$$ λ 2 , 1 ( G ) of $$G$$ G is the minimum range of labels over all such labeling. In this article, it is shown that, for an interval graph $$G$$ G , the upper bound of $$\lambda _{2,1}(G)$$ λ 2 , 1 ( G ) is $$\Delta +\omega $$ Δ + ω , where $$\Delta $$ Δ and $$\omega $$ ω represents the maximum degree of the vertices and size of maximum clique respectively. An $$O(m+n)$$ O ( m + n ) time algorithm is also designed to $$L(2,1)$$ L ( 2 , 1 ) -label a connected interval graph, where $$m$$ m and $$n$$ n represent the number of edges and vertices respectively. Extending this idea it is shown that $$\lambda _{2,1}(G)\le \Delta +3\omega $$ λ 2 , 1 ( G ) ≤ Δ + 3 ω for circular-arc graph.

Glenn S. Solomon - One of the best experts on this subject based on the ideXlab platform.

Richard P. Mirin - One of the best experts on this subject based on the ideXlab platform.

  • Photon-number-discriminating detection using a quantum-dot, optically gated, field-effect transistor
    Nature Photonics, 2007
    Co-Authors: Eric J Gansen, M. B. Greene, M.-y. Su, S.w. Nam, D. Rosenberg, T.e. Harvey, M A Rowe, Robert Henry Hadfield, Richard P. Mirin
    Abstract:

    Detectors with the capability to directly measure the photon number of a pulse of light1, 2, 3 enable linear optics quantum computing4, affect the security of quantum communications5, and can be used to characterize6, 7, 8 and herald9 non-classical states of light. Here, we demonstrate the photon-number-resolving capabilities of a quantum-dot, optically gated, field-effect transistor that uses quantum dots as optically addressable floating gates in a GaAs/Al0.2Ga0.8As -doped field-effect transistor. When the active area of the detector is illuminated, photo-generated carriers trapped by quantum dots screen the gate field, causing a persistent change in the channel current that is proportional to the number of confined carriers. Using weak laser pulses, we show that discrete numbers of trapped carriers produce well resolved changes in the channel current. We demonstrate that for a mean photon number of 1.1, decision regions can be defined such that the field-effect transistor determines the number of detected photons with a probability of accuracy greater than 83%.