Graph Invariants and Large Cycles: A Survey
Graph invariants provide a powerful analytical tool for investigation of abstract substructures of graphs. This paper is devoted to large cycle substructures, namely, Hamilton, longest and dominating cycles and some generalized cycles including Hamilton and dominating cycles as special cases. In thi...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/206404 |
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| _version_ | 1832556406144761856 |
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| author | Zh. G. Nikoghosyan |
| author_facet | Zh. G. Nikoghosyan |
| author_sort | Zh. G. Nikoghosyan |
| collection | DOAJ |
| description | Graph invariants provide a powerful analytical tool for investigation of abstract substructures of graphs. This paper is devoted to large cycle substructures, namely, Hamilton, longest and dominating cycles and some generalized cycles including Hamilton and dominating cycles as special cases. In this paper, we have collected 36 pure algebraic relations between basic (initial) graph invariants ensuring the existence of a certain type of large cycles. These simplest kind of relations having no forerunners in the area actually form a source from which nearly all possible hamiltonian results (including well-known Ore's theorem, Posa's theorem, and many other generalizations) can be developed further by various additional new ideas, generalizations, extensions, restrictions, and structural limitations. |
| format | Article |
| id | doaj-art-b3ac2d4ff1e845fa950d98022d724bd8 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-b3ac2d4ff1e845fa950d98022d724bd82025-02-03T05:45:34ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252011-01-01201110.1155/2011/206404206404Graph Invariants and Large Cycles: A SurveyZh. G. Nikoghosyan0Institute for Informatics and Automation Problems, National Academy of Sciences, P. Sevak 1, Yerevan 0014, ArmeniaGraph invariants provide a powerful analytical tool for investigation of abstract substructures of graphs. This paper is devoted to large cycle substructures, namely, Hamilton, longest and dominating cycles and some generalized cycles including Hamilton and dominating cycles as special cases. In this paper, we have collected 36 pure algebraic relations between basic (initial) graph invariants ensuring the existence of a certain type of large cycles. These simplest kind of relations having no forerunners in the area actually form a source from which nearly all possible hamiltonian results (including well-known Ore's theorem, Posa's theorem, and many other generalizations) can be developed further by various additional new ideas, generalizations, extensions, restrictions, and structural limitations.http://dx.doi.org/10.1155/2011/206404 |
| spellingShingle | Zh. G. Nikoghosyan Graph Invariants and Large Cycles: A Survey International Journal of Mathematics and Mathematical Sciences |
| title | Graph Invariants and Large Cycles: A Survey |
| title_full | Graph Invariants and Large Cycles: A Survey |
| title_fullStr | Graph Invariants and Large Cycles: A Survey |
| title_full_unstemmed | Graph Invariants and Large Cycles: A Survey |
| title_short | Graph Invariants and Large Cycles: A Survey |
| title_sort | graph invariants and large cycles a survey |
| url | http://dx.doi.org/10.1155/2011/206404 |
| work_keys_str_mv | AT zhgnikoghosyan graphinvariantsandlargecyclesasurvey |