# On degree sets and the minimum orders in bipartite graphs

• Volume: 34, Issue: 2, page 383-390
• ISSN: 2083-5892

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## Abstract

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

## How to cite

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Y. Manoussakis, and H.P. Patil. "On degree sets and the minimum orders in bipartite graphs." Discussiones Mathematicae Graph Theory 34.2 (2014): 383-390. <http://eudml.org/doc/268007>.

@article{Y2014,
abstract = {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},
author = {Y. Manoussakis, H.P. Patil},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {degree sets; unicyclic graphs},
language = {eng},
number = {2},
pages = {383-390},
title = {On degree sets and the minimum orders in bipartite graphs},
url = {http://eudml.org/doc/268007},
volume = {34},
year = {2014},
}

TY - JOUR
AU - Y. Manoussakis
AU - H.P. Patil
TI - On degree sets and the minimum orders in bipartite graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2014
VL - 34
IS - 2
SP - 383
EP - 390
AB - 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
LA - eng
KW - degree sets; unicyclic graphs
UR - http://eudml.org/doc/268007
ER -

## References

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2. [2] S.F. Kapoor, A.D. Polimeni and C.W. Wall, Degree sets for graphs, Fund. Math. XCV (1977) 189-194. Zbl0351.05129
3. [3] Y. Manoussakis, H.P. Patil and V. Sankar, Further results on degree sets for graphs, AKCE Int. J. Graphs Comb. 1 (2004) 77-82. Zbl1065.05032
4. [4] Y. Manoussakis and H.P. Patil, Bipartite graphs and their degree sets, R.C. Bose Centenary Symposium on Discrete Mathematics and Applications, (Kolkata India, 15-21 Dec. 2002), Electron. Notes Discrete Math. 15 (2003) 125. doi:10.1016/S1571-0653(04)00554-2[Crossref]
5. [5] S. Pirzada, T.A. Naikoo, and F.A. Dar, Degree sets in bipartite and 3-partite graphs, Orient. J. Math Sciences 1 (2007) 39-45. Zbl1144.05308
6. [6] A. Tripathi and S. Vijay, On the least size of a graph with a given degree set, Discrete Appl. Math. 154 (2006) 2530-2536. doi:10.1016/j.dam.2006.04.003 [Crossref] Zbl1110.05024

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