Research articles
ScienceAsia 40 (2014): 313-316 |doi:
10.2306/scienceasia1513-1874.2014.40.313
On the minimum skew rank of graphs
Yanna Wanga, Bo Zhoub,*
ABSTRACT: The minimum skew rank mr−(𝔽,G) of a graph G over a field 𝔽 is the smallest possible rank among all skew symmetric matrices over 𝔽 whose (i,j)th entry (for i≠j) is non-zero whenever ij is an edge in G and is zero otherwise. We characterize the graphs G with cut vertices over an infinite field 𝔽 such that mr−(𝔽,G)=4 determine the minimum skew rank of k-paths over a field 𝔽, and show that mr−(𝔽,G)=2β(G)=MR−(𝔽,G) for a connected graph G with no even cycles and a field 𝔽 where β(G) is the matching number of G, and MR−(𝔽,G) is the largest possible rank among all skew symmetric matrices over 𝔽.
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| a |
Public Courses Department, Hubei Industrial Polytechnic, Shiyan 442000, China |
| b |
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China |
* Corresponding author, E-mail: zhoubo@scnu.edu.cn
Received 9 Jun 2013, Accepted 21 Mar 2014
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