On ordering of minimal energies in bicyclic signed graphs

Abstract

Let S = (G, σ) be a signed graph of order n and size m and let x1, x2, ..., xn be the eigenvalues of S. The energy of S is defined as ɛ ( S ) = ∑ j = 1 n | x j | \varepsilon \left( S \right) = \sum\limits_{j = 1}^n {\left| {{x_j}} \right|} . A connected signed graph is said to be bicyclic if m=n + 1. In this paper, we determine the bicyclic signed graphs with first 20 minimal energies for all n ≥ 30 and with first 16 minimal energies for all 17 ≤ n ≤ 29.