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    General Trinajstić Index

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    In memory of the outstanding theoretical chemist Nenad Trinajstić, Furtula introduced a new distance-based molecular structure descriptor "Trinajstić index" in chemical graph theory. In this paper, we propose the general Trinajstić index, and give the calculation formula of the general Trinajstić index for double-star graphs, double brooms, Kragujevac trees, firefly graphs and wheel graphs. As an application, we calculate the general Trinajstić index for some hydrocarbons

    Tunable optical multistability induced by a single cavity mode in cavity quantum electrodynamics system

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    A tunable optical multistability scheme based on a single cavity mode coupled with two separate atomic transitions in an atom-cavity system is proposed and demonstrated. Under the collective strong coupling condition, multiple polariton eigenstates of the atom-cavity system are produced. The threshold and optical multistability curve can be tuned freely by system parameters in a broadband range. Moreover, a certain bistability region of the system is split to two bistability regions due to destructive quantum interference induced by an extra weak control field. Compared to traditional optical multistabilities created by two or more light fields, the proposed optical multistability scheme has compactness and is easy to be miniaturized. The proposed scheme is useful for manufacturing integrated application of multi-state all-optical logic devices and constructing basic elements of all-optical communication networks
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