Geodesic
Nordhaus-Gaddum-Type Results for Resistance Distance-Based Graph Invariants
Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 3, pp. 695-707

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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.
Keywords: resistance distance, Kirchhoff index, additive degree-Kirchhoff index, multiplicative degree-Kirchhoff index, Nordhaus-Gaddum-type result 
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     author = {Das, Kinkar Ch. and Yang, Yujun and Xu, Kexiang},
     title = {Nordhaus-Gaddum-Type {Results} for {Resistance} {Distance-Based} {Graph} {Invariants}},
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     url = {http://geodesic.mathdoc.fr/item/DMGT_2016_36_3_a13/}
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Das, Kinkar Ch.; Yang, Yujun; Xu, Kexiang. Nordhaus-Gaddum-Type Results for Resistance Distance-Based Graph Invariants. Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 3, pp. 695-707. http://geodesic.mathdoc.fr/item/DMGT_2016_36_3_a13/