Exact values of girth for some graphs D(k,q) and upper bounds of the order of cages
Let q be a prime power and k∈{5,7,9,11}. In this paper it is shown that the girth of a graph D(k,q) is equal to k+5. As a consequence, explicit examples of graphs which provide the best known upper bounds of the order of (r,g)-cages, r≥5, g∈{10,14,16}, are given.
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2008 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2008
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/152392 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Exact values of girth for some graphs D(k,q) and upper bounds of the order of cages / P. Pikuta // Algebra and Discrete Mathematics. — 2008. — Vol. 7, № 2. — С. 83–88. — Бібліогр.: 13 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862605154424979456 |
|---|---|
| author | Pikuta, P. |
| author_facet | Pikuta, P. |
| citation_txt | Exact values of girth for some graphs D(k,q) and upper bounds of the order of cages / P. Pikuta // Algebra and Discrete Mathematics. — 2008. — Vol. 7, № 2. — С. 83–88. — Бібліогр.: 13 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | Let q be a prime power and k∈{5,7,9,11}. In this paper it is shown that the girth of a graph D(k,q) is equal to k+5. As a consequence, explicit examples of graphs which provide the best known upper bounds of the order of (r,g)-cages, r≥5, g∈{10,14,16}, are given.
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| first_indexed | 2025-11-28T11:07:29Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-152392 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-28T11:07:29Z |
| publishDate | 2008 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Pikuta, P. 2019-06-10T19:05:12Z 2019-06-10T19:05:12Z 2008 Exact values of girth for some graphs D(k,q) and upper bounds of the order of cages / P. Pikuta // Algebra and Discrete Mathematics. — 2008. — Vol. 7, № 2. — С. 83–88. — Бібліогр.: 13 назв. — англ. 1726-3255 2000 Mathematics Subject Classification:05C35, 05C38. https://nasplib.isofts.kiev.ua/handle/123456789/152392 Let q be a prime power and k∈{5,7,9,11}. In this paper it is shown that the girth of a graph D(k,q) is equal to k+5. As a consequence, explicit examples of graphs which provide the best known upper bounds of the order of (r,g)-cages, r≥5, g∈{10,14,16}, are given. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Exact values of girth for some graphs D(k,q) and upper bounds of the order of cages Article published earlier |
| spellingShingle | Exact values of girth for some graphs D(k,q) and upper bounds of the order of cages Pikuta, P. |
| title | Exact values of girth for some graphs D(k,q) and upper bounds of the order of cages |
| title_full | Exact values of girth for some graphs D(k,q) and upper bounds of the order of cages |
| title_fullStr | Exact values of girth for some graphs D(k,q) and upper bounds of the order of cages |
| title_full_unstemmed | Exact values of girth for some graphs D(k,q) and upper bounds of the order of cages |
| title_short | Exact values of girth for some graphs D(k,q) and upper bounds of the order of cages |
| title_sort | exact values of girth for some graphs d(k,q) and upper bounds of the order of cages |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/152392 |
| work_keys_str_mv | AT pikutap exactvaluesofgirthforsomegraphsdkqandupperboundsoftheorderofcages |