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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 ij) 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