Hosam Abdo

Graphs with maximal irregularity

Albertson (3) has defined the irregularity of a simple undirected graph G = (V; E) as irr(G) =

The irregularity of graphs under graph operations

Abstract The irregularity of a simple undirected graph G was defined by Albertson [5] as irr(G) = ∑uv∈E(G) |dG(u) − dG(v)|, where dG(u) denotes the degree of a vertex u ∈ V (G). In this paper we consider the irregularity of graphs under several graph operations including join, Cartesian product, direct product, strong product, corona product, lexicographic product, disjunction and sym- metric difference. We give exact expressions or (sharp) upper bounds on the irregularity of graphs under the above mentioned operations

Graphs with Maximal Irregularity

Abstract A natural extension of the well-known Albertson irregularity index is the recently introduced σ irregularity index. For a simple graph G with an edge set E ( G ) , the σ irregularity index is defined as σ ( G ) = ∑ u v ∈ E ( G ) ( d G ( u ) − d G ( v ) ) 2 , where d G ( v ) denotes the degree of the vertex v of G . Here, we characterize general graphs with maximal σ irregularity. We also present lower bounds on the maximal σ irregularity of graphs with fixed minimal and/or maximal vertex degrees.