𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The minimum rank of matrices and the equivalence class graph

✍ Scribed by Rosàrio Fernandes; Cecı´lia Perdigão


Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
208 KB
Volume
427
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.


📜 SIMILAR VOLUMES


The minimum rank of symmetric matrices d
✍ Shaun M. Fallat; Leslie Hogben 📂 Article 📅 2007 🏛 Elsevier Science 🌐 English ⚖ 331 KB

The minimum rank of a simple graph G is defined to be the smallest possible rank over all symmetric real matrices whose ijth entry (for i / = j ) is nonzero whenever {i, j } is an edge in G and is zero otherwise. This paper surveys the current state of knowledge on the problem of determining the min

Switching classes of directed graphs and
✍ Ying Cheng 📂 Article 📅 1986 🏛 Elsevier Science 🌐 English ⚖ 781 KB

In this paper, we define and study the switching classes of directed graphs. The definition is a generalization of both Van Lint and Seidel's switching classes of graphs and Cameron's switching classes of tournaments. We actually do it in a general way so that Wells" signed switching classes of grap

On the minimum rank of the join of graph
✍ Francesco Barioli; Shaun Fallat 📂 Article 📅 2007 🏛 Elsevier Science 🌐 English ⚖ 184 KB

For a given undirected graph G, the minimum rank of G is defined to be the smallest possible rank over all real symmetric matrices A whose (i, j )th entry is nonzero whenever i / = j and {i, j } is an edge in G. In this work we consider joins and unions of graphs, and characterize the minimum rank o

A note on universally optimal matrices a
✍ Liang-Hao Huang; Gerard J. Chang; Hong-Gwa Yeh 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 164 KB

For a simple graph G on n vertices, the minimum rank of G over a field F, written as mr F (G), is defined to be the smallest possible rank among all n × n symmetric matrices over F whose (i, j)th entry (for i / = j) is nonzero whenever {i, j} is an edge in G and is zero otherwise. A symmetric integ