Tutte uniqueness of line graphs |
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Authors: | Anna de Mier |
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Affiliation: | Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Jordi Girona, 1-3, 08034 Barcelona, Spain |
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Abstract: | We prove that if a graph H has the same Tutte polynomial as the line graph of a d-regular, d-edge-connected graph, then H is the line graph of a d-regular graph. Using this result, we prove that the line graph of a regular complete t-partite graph is uniquely determined by its Tutte polynomial. We prove the same result for the line graph of any complete bipartite graph. |
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Keywords: | Tutte polynomial Line graph Tutte uniqueness |
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