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Nanonetwork is defined as a mathematical model of nanosize objects with biological, physical and chemical attributes, which are interconnected within certain dynamical process. To demonstrate the potentials of this modeling approach for quantitative study of complexity at nanoscale, in this survey, we consider three kinds of nanonetworks: Genes of a yeast are connected by weighted links corresponding to their coexpression along the cell cycle; Gold nanoparticles, arranged on a substrate, are linked...
Two decades ago, resistance distance was introduced to characterize “chemical distance” in (molecular) graphs. In this paper, we consider three resistance distance-based graph invariants, namely, the Kirchhoff index, the additive degree-Kirchhoff index, and the multiplicative degree-Kirchhoff index. Some Nordhaus-Gaddum-type results for these three molecular structure descriptors are obtained. In addition, a relation between these Kirchhoffian indices is established.
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