Some New Lower Bounds on Laplacian Resolvent Energy of Graphs

Abstract:

Let G be a simple connected graph of order n ≥ 3 with m edges and the vertex degree sequence d₁ ≥ d₂ ≥ ⋯ ≥ d_n. The Laplacian resolvent energy of G is defined as RL(G) = ∑ⁿ_i=1 1/(n+1−μ_i), where μ₁ ≥ μ₂ ≥ ⋯ ≥ μ_n−1 > μ_n = 0, are Laplacian eigenvalues of G. In this paper, we find some new lower bounds for RL(G) involving the vertex degrees d₁, d₂, d_n−1, d_n and various degree-based graph invariants.