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

Let GG be a connected regular graph. Denoted by t(G)t(G) and Kf(G)Kf(G) the total graph and Kirchhoff index of GG, 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(G), where GG is a regular graph. Consequently, by using Kf(G)Kf(G), we give an expression on Kf(t(G))Kf(t(G)) and a lower bound on Kf(t(G))Kf(t(G)) of a regular graph GG, which correct Theorem 3.7 and Corollary 3.8 in Gao et al. (2012)  [2].