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Linear and Multilinear Algebra Volume 64, 2016 - Issue 5
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Articles

A characterization of signed planar graphs with rank at most 4

Fenglei TianDepartment of Mathematics, China University of Mining and Technology, Xuzhou, China.View further author information
,
Dengyin WangDepartment of Mathematics, China University of Mining and Technology, Xuzhou, China.Correspondence[email protected]
View further author information
&
Min ZhuDepartment of Mathematics, China University of Mining and Technology, Xuzhou, China.View further author information
Pages 807-817 | Received 10 May 2013, Accepted 21 May 2015, Published online: 08 Jul 2015

References

  • Fallat S, Hogben L. The minimum rank of symmetric matrices described by a graph: a survey. Linear Algebra Appl. 2007;426:558–582.
  • Tan X, Liu B. On the nullity of unicyclic graphs. Linear Algebra Appl. 2005;408:212–220.
  • Cheng GJ, Huang L-H, Yeh H-G. A characterization of graphs with rank 4. Linear Algebra Appl. 2011;434:1793–1798.
  • Cheng GJ, Huang L-H, Yeh H-G. A characterization of graphs with rank 5. Linear Algebra Appl. 2012;436:4241–4250.
  • Sciriha I. On the rank of graphs. In: Alavi Y, Lick DR, Schwenk A, editors. Combinatorics, graph theory and algorithms. Vol. 2. Kalamazoo (MI): New Issue Press, Western Michigan University; 1999. p. 769–778.
  • Borovićanin B, Gutman I. Nullity of graphs. In: Cvetković D, Gutman I, editors. Applications of graph spectra. Belgrade: Mathematical Institute; 2009. p. 107–122.
  • Fan Y-Z, Qian K-S. On the nullity of bipartite graphs. Linear Algebra Appl. 2009;430:2943–2949.
  • Li S. On the nullity of graphs with pendant vertices. Linear Algebra Appl. 2008;429:1619–1628.
  • Gong S-C, Fan Y-Z, Yin Z-X. On the nullity of graphs with pendent trees. Linear Algebra Appl. 2010;433:1374–1380.
  • Guo J-M, Yan W, Yeh Y-N. On the nullity and the matching number of unicyclic graphs. Linear Algebra Appl. 2009;431:1293–1301.
  • Hu S, Tan X, Liu B. On the nullity of bicyclic graphs. Linear Algebra Appl. 2008;429:1387–1391.
  • Li W, Chang A. Describing the nonsingular unicyclic graph. J. Math. Study. 2007;40:442–445.
  • Fan Y-Z, Wang Y, Wang Y. A note on the nullity of unicyclic signed graphs. Linear Algebra Appl. 2013;438:1193–1200.
  • Zaslavsky T. Signed graphs. Discrete Appl. Math. 1982;4:47–74.
  • Cvetković D, Doob M, Sachs H. Spectra of graphs. 3rd ed. Heidelberg: Johann Ambrosius Barth; 1995.
  • Fan Y-Z. Largest eigenvalue of a unicyclic mixed graph. Appl. Math. J. Chinese Univ. Ser. B. 2004;19:140–148.

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