Elsevier

Discrete Applied Mathematics

Volume 233, 31 December 2017, Pages 224-230
Discrete Applied Mathematics

The asymptotic behavior of (degree-)Kirchhoff indices of iterated total graphs of regular graphs

https://doi.org/10.1016/j.dam.2017.08.019Get rights and content
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Abstract

Let G be a simple connected graph. Denote the Kirchhoff index and the degree-Kirchhoff index of G by Kf(G) and Kf(G), respectively. This paper considers the asymptotic behavior of Kf(Tk(G)) and Kf(Tk(G)) of the iterated total graph Tk(G) of an r-regular graph G. We show that the asymptotic behavior of these indices is independent of the structure of G and only dependent on the degree and the number of vertices of G.

Keywords

Kirchhoff index
Degree-Kirchhoff index
Regular graph
Total graph

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