Geodesic
On degree sets and the minimum orders in bipartite graphs
Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 2, pp. 383-390

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For any simple graph G, let D(G) denote the degree set deg_G(v) : v ∈ V (G). Let S be a finite, nonempty set of positive integers. In this paper, we first determine the families of graphs G which are unicyclic, bipartite satisfying D(G) = S, and further obtain the graphs of minimum orders in such families. More general, for a given pair (S, T) of finite, nonempty sets of positive integers of the same cardinality, it is shown that there exists a bipartite graph B(X, Y) such that D(X) = S, D(Y ) = T and the minimum orders of different types are obtained for such graphs
Keywords: degree sets, unicyclic graphs 
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Manoussakis, Y.; Patil, H.P. On degree sets and the minimum orders in bipartite graphs. Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 2, pp. 383-390. http://geodesic.mathdoc.fr/item/DMGT_2014_34_2_a11/