Bicyclic graphs with minimum energy

Abstract

If λ₁, λ₂,…,λ_n are the eigenvalues of a graph G, then the energy of this graph is denned as . For n⩾6, let be the graph obtained by joining n−5 pendant vertices to a vertex of degree three of the complete bipartite graph K ₂. We show that for all values of n⩾6, S ^4,4 _n has the minimal energy among all n vertex connected bicyclic graphs with at most one odd cycle.