Summary: For a simple connected graph \(G\) of order \(n\), the Laplacian-energy-like invariant and the Kirchhoff index are calculated by \(LEL(G) = \sum^{n-1}_{i=1}\sqrt{\mu_i}\) and \(K f(G) =n \sum^{n-1}_{i=1} 1/\mu_i\), respectively, where \(\mu_1,\mu_2,\dots,\mu_{n-1},\mu_n= 0\) are the Laplacian eigenvalues of \(G\). We obtain a sharp upper bound for \(K f \) and a sharp lower bound for \(LEL\). Further, we obtain upper and lower bounds for \(LEL\) and \(K f\) for graphs \(C(G)\) (the clique-inserted graph or para-line graph), \(R(G)\) (obtained by changing each edge of \(G\) into a triangle), and \(H(G)\) (obtained by inserting a new vertex on each edge of \(G\) and by joining two new vertices if they lie on adjacent edges of \(G\)), as well as for the line graph of a semiregular graph.