Note on non-regular graphs with minimal total irregularity

Let G be a graph with vertex set V(G). The total irregularity of G is defined as irr(t) (G) Sigma({u,v}subset of V(G)) vertical bar deg(G)(u) - deg(G)(v)vertical bar, where deg(G)(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. (C) 2019 Elsevier Inc. All rights reserved.