Graphical Representations of Graphic Frame Matroids.
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| Title: | Graphical Representations of Graphic Frame Matroids. |
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| Authors: | Chen, Rong1 rongchen@fzu.edu.cn, DeVos, Matthew2 mdevos@sfu.ca, Funk, Daryl2 daryl.funk@gmail.com, Pivotto, Irene3 irene.pivotto@uwa.edu.au |
| Source: | Graphs & Combinatorics. Nov2015, Vol. 31 Issue 6, p2075-2086. 12p. |
| Subjects: | Representations of graphs, Frames (Combinatorial analysis), Matroids, Isomorphism (Mathematics), Graph theory, Mathematical analysis |
| Abstract: | A frame matroid $$M$$ is graphic if there is a graph $$G$$ with cycle matroid isomorphic to $$M$$ . In general, if there is one such graph, there will be many. Zaslavsky has shown that frame matroids are precisely those having a representation as a biased graph; this class includes graphic matroids, bicircular matroids, and Dowling geometries. Whitney characterized which graphs have isomorphic cycle matroids, and Matthews characterized which graphs have isomorphic graphic bicircular matroids. In this paper, we give a characterization of which biased graphs give rise to isomorphic graphic frame matroids. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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