2019/03/04 by Enide Andrade, Andrade, Enide, Juan R. Carmona +5
Computer Science · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Matrix Theory and Algorithms #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.1903.01326
openalex publication_date 2019/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let R be a Hermitian matrix. The energy of R, E(R), corresponds to the sum of the absolute values of its eigenvalues. In this work it is obtained two lower bounds for E(R). The first one generalizes a lower bound obtained by Mc Clellands for the energy of graphs in 1971 to the case of Hermitian matrices and graphs with a given nullity. The second one generalizes a lower bound obtained by K. Das, S. A. Mojallal and I. Gutman in 2013 to symmetric non-negative matrices and graphs with a given nullity. The equality cases are discussed. These lower bounds are obtained for graphs with m edges and some examples are provided showing that, some obtained bounds are incomparable with the known lower bound for the energy 2√(m). Another family of lower bounds are obtained from an increasing sequence of lower bounds for the spectral radius of a graph. The bounds are stated for singular and non-singular graphs.