Geodesic
The irregularity of graphs under graph operations
Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 2, pp. 263-278

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The irregularity of a simple undirected graph G was defined by Albertson [5] as irr(G) = ∑_uv∈E(G) |dG(u) − dG(v)|, where d_G(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 symmetric difference. We give exact expressions or (sharp) upper bounds on the irregularity of graphs under the above mentioned operations
Keywords: irregularity of graphs, total irregularity of graphs, graph operations, Zagreb indices 
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     title = {The irregularity of graphs under graph operations},
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Abdo, Hosam; Dimitrov, Darko. The irregularity of graphs under graph operations. Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 2, pp. 263-278. http://geodesic.mathdoc.fr/item/DMGT_2014_34_2_a4/