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

Let G be a simple connected graph. Denote the Kirchhoff index and the degree-Kirchhoff index of G by K f ( G ) and K f ∗ ( G ) , respectively. This paper considers the asymptotic behavior of K f ( T k ( G ) ) and K f ∗ ( T k ( G ) ) of the iterated total graph T k ( 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 .