A study on total irregularities of certain graphs and digraphs

International audienceThe total irregularity of a simple undirected graph G is denoted by irr t (G) and is defined as irr t (G) = 1 2 ∑ u,v∈V(G) �d(u) − d(v)�. In this paper, we introduce the notion of edge-transformation in relation to total irregularity of simple graphs with at least one cut edge as well as an edge-joint between two graphs. We also introduce the notion of total irregularity with respect to in-degree and out-degree in directed graphs. We also introduce the concept of total irregularity in respect of in-degree and out-degree in simple directed graphs. These invariants are called total in-irregularity and total out-irregularity, respectively. In this paper, we initiate a study on these parameters of given simple undirected graphs and simple digraphs