Abstract: Let G be a simple graph of order n and let L be its Laplacian matrix. Eigenvalues of the matrix L are denoted by μ1, μ2, • • • , μn and it is assumed that μ1 > μ2 > • • • > μn. The Laplacian resolvent energy and Kirchhoff index of the graph G are defined as RL(G)=∑▒〖1/(n+1-μi)〗 and Kf(G)=n∑_(i=1)^(n-1)▒〖1/μi〗, respectively. In this paper, we derive some bounds on the invariant RL(G) and establish a relation between RL(G) and Kf (G). https://phaidrabg.bg.ac.rs/o:28912 ISSN: 2664-2557 info:eu-repo/semantics/article 2019 Keywords: Graph energy; Laplacian resolvent energy; Kirchhoff index All rights reserved application/pdf 355682 bytes eng A note on the Laplacian resolvent energy, Kirchhoff index and their relations Zogić, Emir Glogić, Eldin Discrete Mathematics Letters 2