Geodesic
Line graphs: their maximum nullities and zero forcing numbers
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 3, pp. 743-755

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The maximum nullity over a collection of matrices associated with a graph has been attracting the attention of numerous researchers for at least three decades. Along these lines various zero forcing parameters have been devised and utilized for bounding the maximum nullity. The maximum nullity and zero forcing number, and their positive counterparts, for general families of line graphs associated with graphs possessing a variety of specific properties are analysed. Building upon earlier work, where connections to the minimum rank of line graphs were established, we verify analogous equations in the positive semidefinite cases and coincidences with the corresponding zero forcing numbers. Working beyond the case of trees, we study the zero forcing number of line graphs associated with certain families of unicyclic graphs.
DOI : 10.1007/s10587-016-0290-x
Classification : 05C50, 15A03, 15A18
Keywords: maximum nullity; zero forcing number; positive zero forcing number; line graphs; matrix; tree; positive semidefinite matrix; unicyclic graph 
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Fallat, Shaun; Soltani, Abolghasem. Line graphs: their maximum nullities and zero forcing numbers. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 3, pp. 743-755. doi: 10.1007/s10587-016-0290-x

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