Geodesic
On graphs with graphic imbalance sequences
Algebra and discrete mathematics, Tome 18 (2014) no. 1, pp. 97-108.

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The imbalance of the edge $e=uv$ in a graph $G$ is the value $imb\,_{G}(e)=|d_{G}(u)-d_{G}(v)|$. We prove that the sequence $M_{G}$ of all edge imbalances in $G$ is graphic for several classes of graphs including trees, graphs in which all non-leaf vertices form a clique and the so-called complete extensions of paths, cycles and complete graphs. Also, we formulate two interesting conjectures related to graphicality of $M_{G}$.
Keywords: edge imbalance, graph irregularity, graphic sequence. 
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Sergiy Kozerenko; Volodymyr Skochko. On graphs with graphic imbalance sequences. Algebra and discrete mathematics, Tome 18 (2014) no. 1, pp. 97-108. http://geodesic.mathdoc.fr/item/ADM_2014_18_1_a9/

[1] H. Abdo, N. Cohen and D. Dimitrov, Bounds and computation of irregularity of a graph, Preprint, 2012, arXiv: 1207.4804

[2] M. O. Albertson, “The irregularity of a graph”, Ars Comb., 46 (1997), 219–225 | MR | Zbl

[3] F. K. Bell, “A note on the irregularity of graphs”, Lin. Algebra Appl., 161 (1992), 45–54 | DOI | MR | Zbl

[4] P. Erdos, T. Gallai, “Graphs with prescribed degrees of vertices”, Mat. Lapok, 11 (1960), 264–274

[5] F. Goldberg, A spectral bound for graph irregularity, Preprint, 2013, arXiv: 1308.3867

[6] P. Hansen, H. Melot, “Variable neighborhood search for extremal graphs 9. Bounding the irregularity of a graph”, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 69, 2005, 253–264 | MR | Zbl

[7] M. A. Henning, D. Rautenbach, “On the irregularity of bipartite graphs”, Discrete Math., 307 (2007), 1467–1472 | DOI | MR | Zbl

[8] M. Tavakoli, F. Rahbarnia, M. Mirzavaziri, A. R. Ashrafi and I. Gutman, “Extremely irregular graphs”, Kragujevac J. Mat., 37:1 (2013), 135–139 | MR | Zbl

[9] W. Luo, B. Zhou, “On irregularity of graphs”, Ars Comb., 88 (2008), 55–64 | MR | Zbl

[10] W. Luo, B. Zhou, “On the irregularity of trees and unicyclic graphs with given matching number”, Util. Math., 83 (2010), 141–147 | MR | Zbl