Note on non-regular graphs with minimal total irregularity

Abstract Let G be a graph with vertex set V(G). The total irregularity of G is defined as i r r t ( G ) = ∑ { u , v } ⊆ V ( G ) | d e g G ( u ) − d e g G ( v ) | , where degG(v) is the degree of the vertex v of G. The aim of this paper is to present some bounds for this graph invariant. A new simple proof for a recently proposed conjecture on total irregularity of graphs is also presented.