Tree Covers of Graphs and their Linear Preservers

被引：0

作者：

Beasley, LeRoy B. ^{[1
]}

机构：

[1] Dept. of Mathematics and Statistics, Utah State University, Logan, Utah Clocktower Plaza#317, 550 North Main, Box C3, Logan, 84321, UT

来源：

Journal of Combinatorial Mathematics and Combinatorial Computing | 2024年 / 122卷

关键词：

Linear preserver; Maximim nullity; Tree Cover; Tree cover number;

D O I：

10.61091/jcmcc122-12

中图分类号：

学科分类号：

摘要：

Let G be an undirected graph. A vertex tree cover of G is a collection of trees such that every vertex of G is incident with at least one tree. Similarly, an edge tree cover is a collection of trees such that every edge of G is contained in at least one tree. The tree cover number is defined as the minimum number of trees required in such a cover. In this paper, we demonstrate that when considering specific types of tree covers, only vertex permutations act as linear operators that preserve the tree cover number of G. © 2024 the Author(s), licensee Combinatorial Press.

引用

页码：149 / 155

页数：6

共 6 条

[1] Barioli F., Fallat S. M., Mitchell L. H., Narayan S. K., Minimum semidefinite rank of outerplanar graphs and the tree cover number, Electronic Journal of Linear Algebra, 22, pp. 10-21, (2011)
[2] Bozeman C., Catral M., Cook B., Gonzalez O. E., Reinhardt C., On the tree cover number of a graph, Involve, 10, 5, pp. 767-779, (2017)
[3] Domagalski R., Narayan S. K., Tree cover number and maximum semidefinite nullity of some graph classes, Electronic Journal of Linear Algebra, 36, pp. 678-693, (2020)
[4] Fallat S. M., Hogben L., The minimum rank of symmetric matrices described by a graph: A survey, Linear Algebra and Its Applications, 426, 2-3, pp. 558-582, (2007)
[5] Bondy J. A., Murthy U. S. R., Graph Theory (Graduate Texts in Mathematics), (2008)
[6] Beasley L. B., Pullman N. J., Linear operators preserving properties of graphs, Congressus Numerantium, 70, pp. 105-112, (1990)

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