A study on total irregularities of certain graphs and digraphs

Johan Kok (1) , Sudev Naduvath (2)

1 Centre for Studies in Discrete Mathematics
2 Christ University, Bangalore, India

The 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.

Mots clés: branch-transformation; edge-transformation; edge-joint; total in-irregularity; total out-irregularity; Total irregularity

Domaines: Mathématiques [math]; Combinatoire [math.CO]

Johan Kok, Sudev Naduvath. A study on total irregularities of certain graphs and digraphs. Cogent Mathematics & Statistics, 2016, 3 (1), ⟨10.1080/23311835.2016.1179708⟩. ⟨hal-02263315⟩