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On degree sets and the minimum orders in bipartite graphs

100%

Manoussakis Y., Patil H. P.

Discussiones Mathematicae Graph Theory

2014

tom 34

nr 2

383-390

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) = S, D(Y ) = T and the minimum orders of different types are obtained for such graphs

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Extremum degree sets of irregular oriented graphs and pseudodigraphs

80%

Dziechcińska-Halamoda Z., Majcher Z., Michael J., Skupień Z.

Discussiones Mathematicae Graph Theory

2006

tom 26

nr 2

317-333

A digraph in which any two vertices have distinct degree pairs is called irregular. Sets of degree pairs for all irregular oriented graphs (also loopless digraphs and pseudodigraphs) with minimum and maximum size are determined. Moreover, a method of constructing corresponding irregular realizations of those sets is given.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

1 Dziechcińska-Halamoda Z.

1 Majcher Z.

1 Manoussakis Y.

1 Michael J.

1 Patil H. P.

1 Skupień Z.

1 2014

1 2006

Wyniki wyszukiwania

On degree sets and the minimum orders in bipartite graphs

Extremum degree sets of irregular oriented graphs and pseudodigraphs