Comment on “Kirchhoff index in line,subdivision and total graphs of a regular graph”

Let G$G$ be a connected regular graph. Denoted by t(G)$t\left(G\right)$ and Kf(G)$Kf\left(G\right)$ the total graph and Kirchhoff index of G$G$, respectively. This paper is to point out that Theorem 3.7 and Corollary 3.8 from “Kirchhoff index in line, subdivision and total graphs of a regular graph” [X. Gao, Y.F. Luo, W.W. Liu, Kirchhoff index in line, subdivision and total graphs of a regular graph, Discrete Appl. Math. 160(2012) 560–565] are incorrect, since the conclusion of a lemma is essentially wrong. Moreover, we first show the Laplacian characteristic polynomial of t(G)$t\left(G\right)$, where G$G$ is a regular graph. Consequently, by using Kf(G)$Kf\left(G\right)$, we give an expression on Kf(t(G))$Kf\left(t\left(G\right)\right)$ and a lower bound on Kf(t(G))$Kf\left(t\left(G\right)\right)$ of a regular graph G$G$, which correct Theorem 3.7 and Corollary 3.8 in Gao et al. (2012)  [2].