Line graphs: their maximum nullities and zero forcing numbers

Czechoslovak Mathematical Journal

Shaun Fallat¹  Abolghasem Soltani² 

[1] Department of Mathematics and Statistics, University of Regina, 3737 Wascana Parkway, S4S 0A4 Regina SK, Canada;Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Jalal AleAhmad Nasr No. 7, 14115-134, Tehran, Iran

关键词: maximum nullity;    zero forcing number;    positive zero forcing number;    line graphs;    matrix;    tree;    positive semidefinite matrix;    unicyclic graph;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

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.

【 授权许可】

Unknown