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

Voir la notice de l'article provenant de la source Math-Net.Ru

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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     author = {Sergiy Kozerenko and Volodymyr Skochko},
     title = {On graphs with graphic imbalance sequences},
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     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2014_18_1_a9/}
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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/