| The Triangle-Free Graphs with Rank $6$ |
| Received:December 08, 2013 Revised:April 07, 2014 |
| Key Words:
graph rank nullity.
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| Fund Project:Supported by National Natural Science Foundation of China (Grant Nos.\,11071002; 11371028), Program for New Century Excellent Talents in University (Grant No.\,NCET-10-0001), Key Project of Chinese Ministry of Education (Grant No.\,210091), Scientific Research Fund for Fostering Distinguished Young Scholars of Anhui University (Grant No.\,KJJQ1001), Academic Innovation Team of Anhui University Project (Grant No.\,KJTD001B). |
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| Abstract: |
| The rank of a graph $G$ is defined to be the rank of its adjacency matrix $A(G)$. In this paper we characterize all connected triangle-free graphs with rank $6$. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2014.05.002 |
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