Graphic sequences of trees and a problem of Frobenius

Gautam Gupta; Puneet Joshi; Amitabha Tripathi

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 1, page 49-52
  • ISSN: 0011-4642

Abstract

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We give a necessary and sufficient condition for the existence of a tree of order n with a given degree set. We relate this to a well-known linear Diophantine problem of Frobenius.

How to cite

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Gupta, Gautam, Joshi, Puneet, and Tripathi, Amitabha. "Graphic sequences of trees and a problem of Frobenius." Czechoslovak Mathematical Journal 57.1 (2007): 49-52. <http://eudml.org/doc/31111>.

@article{Gupta2007,
abstract = {We give a necessary and sufficient condition for the existence of a tree of order $n$ with a given degree set. We relate this to a well-known linear Diophantine problem of Frobenius.},
author = {Gupta, Gautam, Joshi, Puneet, Tripathi, Amitabha},
journal = {Czechoslovak Mathematical Journal},
keywords = {graphic; tree-graphic; tree-graphic},
language = {eng},
number = {1},
pages = {49-52},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Graphic sequences of trees and a problem of Frobenius},
url = {http://eudml.org/doc/31111},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Gupta, Gautam
AU - Joshi, Puneet
AU - Tripathi, Amitabha
TI - Graphic sequences of trees and a problem of Frobenius
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 1
SP - 49
EP - 52
AB - We give a necessary and sufficient condition for the existence of a tree of order $n$ with a given degree set. We relate this to a well-known linear Diophantine problem of Frobenius.
LA - eng
KW - graphic; tree-graphic; tree-graphic
UR - http://eudml.org/doc/31111
ER -

References

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  1. On the order of a graph with a given degree set, The Journal of Combinatorial Mathematics and Combinatorial Computing 57 (2006), 157–162. (2006) MR2226692
  2. Graphs with prescribed degrees of vertices, Mat. Lapok 11 (1960), 264–274. (Hungarian) (1960) 
  3. Unsolved Problems in Number Theory. Unsolved Problems in Intuitive Mathematics, Volume  I, Third Edition, Springer-Verlag, New York, 2004. (2004) MR2076335
  4. 10.1137/0110037, J.  SIAM Appl. Math. 10 (1962), 496–506. (1962) MR0148049DOI10.1137/0110037
  5. A remark on the existence of finite graphs, Čas. Pěst. Mat. 80 (1955), 477–480. (Czech) (1955) 
  6. 10.4064/fm-95-3-189-194, Fund. Math. 95 (1977), 189–194. (1977) MR0480200DOI10.4064/fm-95-3-189-194

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