Displaying similar documents to “On connected graphs containing exactly two points of the same degree”

On degree sets and the minimum orders in bipartite graphs

Y. Manoussakis, H.P. Patil (2014)

Discussiones Mathematicae Graph Theory

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For any simple graph G, let D(G) denote the degree set {degG(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)...