Forest decompositions of graphs with cyclomatic number 3
The simple tree polynomials of the basic graphs with cyclomatic number 3 are derived. From these results, explicit formulae for the number of decompositions of the graphs into forests with specified cardinalities are extracted. Explicit expressions are also given for the number of spanning forests a...
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| Format: | Article |
| Language: | English |
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Wiley
1983-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171283000484 |
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| _version_ | 1832568368026091520 |
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| author | E. J. Farrell |
| author_facet | E. J. Farrell |
| author_sort | E. J. Farrell |
| collection | DOAJ |
| description | The simple tree polynomials of the basic graphs with cyclomatic number 3
are derived. From these results, explicit formulae for the number of decompositions of the graphs into forests with specified cardinalities are extracted. Explicit expressions are also given for the number of spanning forests and spanning trees in the graphs. These results complement the results given in [1]. |
| format | Article |
| id | doaj-art-7676582486794cd796a210139991692e |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1983-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-7676582486794cd796a210139991692e2025-02-03T00:59:12ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251983-01-016353554310.1155/S0161171283000484Forest decompositions of graphs with cyclomatic number 3E. J. Farrell0Department of Mathematics, The University of the West Indies, St. Augustine, Trinidad and TobagoThe simple tree polynomials of the basic graphs with cyclomatic number 3 are derived. From these results, explicit formulae for the number of decompositions of the graphs into forests with specified cardinalities are extracted. Explicit expressions are also given for the number of spanning forests and spanning trees in the graphs. These results complement the results given in [1].http://dx.doi.org/10.1155/S0161171283000484tree polynomialsimple tree polynomialforest decompositionbasic graphcyclomatic numberchaincircuitgraphs with trees attached. |
| spellingShingle | E. J. Farrell Forest decompositions of graphs with cyclomatic number 3 International Journal of Mathematics and Mathematical Sciences tree polynomial simple tree polynomial forest decomposition basic graph cyclomatic number chain circuit graphs with trees attached. |
| title | Forest decompositions of graphs with cyclomatic number 3 |
| title_full | Forest decompositions of graphs with cyclomatic number 3 |
| title_fullStr | Forest decompositions of graphs with cyclomatic number 3 |
| title_full_unstemmed | Forest decompositions of graphs with cyclomatic number 3 |
| title_short | Forest decompositions of graphs with cyclomatic number 3 |
| title_sort | forest decompositions of graphs with cyclomatic number 3 |
| topic | tree polynomial simple tree polynomial forest decomposition basic graph cyclomatic number chain circuit graphs with trees attached. |
| url | http://dx.doi.org/10.1155/S0161171283000484 |
| work_keys_str_mv | AT ejfarrell forestdecompositionsofgraphswithcyclomaticnumber3 |