On coefficients of circuit polynomials and characteristic polynomials
Results are given from which expressions for the coefficients of the simple circuit polynomial of a graph can be obtained in terms of subgraphs of the graph. From these are deduced parallel results for the coefficients of the characteristic polynomial of a graph. Some specific results are presented...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1985-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171285000783 |
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| _version_ | 1849691552091209728 |
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| author | E. J. Farrell |
| author_facet | E. J. Farrell |
| author_sort | E. J. Farrell |
| collection | DOAJ |
| description | Results are given from which expressions for the coefficients of the simple
circuit polynomial of a graph can be obtained in terms of subgraphs of the graph. From these are deduced parallel results for the coefficients of the characteristic polynomial of a graph. Some specific results are presented on the parities of the coefficients of characteristic polynomials. A characterization is then determined for graphs in which the number of sets of independent edges is always even. This leads to an interesting link between matching polynomials and characteristic polynomials. Finally explicit formulae are derived for the number of ways of covering two well known
families of graphs with node disjoint circuits, and for the first few coefficients of their characteristic polynomials. |
| format | Article |
| id | doaj-art-e1c0737a0359479b984ba3cfe54e3504 |
| institution | DOAJ |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1985-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e1c0737a0359479b984ba3cfe54e35042025-08-20T03:20:59ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251985-01-018469770510.1155/S0161171285000783On coefficients of circuit polynomials and characteristic polynomialsE. J. Farrell0Department of Mathematics, The University of the West Indies, St. Augustine, Trinidad and TobagoResults are given from which expressions for the coefficients of the simple circuit polynomial of a graph can be obtained in terms of subgraphs of the graph. From these are deduced parallel results for the coefficients of the characteristic polynomial of a graph. Some specific results are presented on the parities of the coefficients of characteristic polynomials. A characterization is then determined for graphs in which the number of sets of independent edges is always even. This leads to an interesting link between matching polynomials and characteristic polynomials. Finally explicit formulae are derived for the number of ways of covering two well known families of graphs with node disjoint circuits, and for the first few coefficients of their characteristic polynomials.http://dx.doi.org/10.1155/S0161171285000783circuit polynomialscircuit cover of a graphsimple circuit polynomialHamiltonian circuitcharacteristic polynomial. |
| spellingShingle | E. J. Farrell On coefficients of circuit polynomials and characteristic polynomials International Journal of Mathematics and Mathematical Sciences circuit polynomials circuit cover of a graph simple circuit polynomial Hamiltonian circuit characteristic polynomial. |
| title | On coefficients of circuit polynomials and characteristic polynomials |
| title_full | On coefficients of circuit polynomials and characteristic polynomials |
| title_fullStr | On coefficients of circuit polynomials and characteristic polynomials |
| title_full_unstemmed | On coefficients of circuit polynomials and characteristic polynomials |
| title_short | On coefficients of circuit polynomials and characteristic polynomials |
| title_sort | on coefficients of circuit polynomials and characteristic polynomials |
| topic | circuit polynomials circuit cover of a graph simple circuit polynomial Hamiltonian circuit characteristic polynomial. |
| url | http://dx.doi.org/10.1155/S0161171285000783 |
| work_keys_str_mv | AT ejfarrell oncoefficientsofcircuitpolynomialsandcharacteristicpolynomials |