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 irrt(G)=∑{u,v}⊆V(G)|degG(u)−degG(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.