Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

GRAPH REPRESENTATIONS OF NORMAL MATRICES

  • LEE SANG-GU (Department of Mathematics Sungkyunkwan University) ;
  • SEOL HAN-GUK (Department of Mathematics Daejin University)
  • Published : 2006.01.01
Download PDF
⟨ Previous Next ⟩

Abstract

We call the bipartite graph G is normal provided the reduced adjacency matrix A of G is normal. In this paper we give graph representations of normal matrices. In addition we shall have the characterization of signed bipartite normal graphs.

Keywords

References

  1. R. A. Brualdi and H. J. Ryser, Combinatorial Matrix Theory, Encyclopedia of Mathematics and its Applications, Cambridge university Press, Cambridge, 1991
  2. I. Csiszar, J. Korner, L. Lovasz, K. Marton, and G. Simonyi, Entropy splitting for antiblocking corners and perfect graphs, Combinatorica 10 (1990), no. 1, 27-40 https://doi.org/10.1007/BF02122693
  3. R. Grone, C. R. Johnson, E. M. Sa, and H. Wolkowicz, Normal matrices, Linear Algebra Appl. 87 (1987), 213-225 https://doi.org/10.1016/0024-3795(87)90168-6
  4. Z. Li, F. Hall, and F. Zhang, Sign patterns of nonnegative normal matrices, Linear Algebra Appl. 254 (1997), 335-354 https://doi.org/10.1016/S0024-3795(96)00469-7
  5. F. Harary, On the notion of balance of a signed graph, Michigan Math. J. 2 (1953-54), 143-146(1955) https://doi.org/10.1307/mmj/1028989917
  6. J. Korner and G. Longo, Two-step encoding of finite sources, IEEE Trans. Information Theory IT-19 (1973), 778-782
  7. B. Y. Wang and F. Zhang, On normal matrices of zeros and ones with fixed row sum, Linear Algebra Appl. 275/276 (1998), 617-626 https://doi.org/10.1016/S0024-3795(97)10040-4
  8. J. H. Yan, K. W. Lih, D. Kuo, and G. J. Chang, Signed degree sequences of signed graphs, J. Graph Theory 26 (1997), no. 2, 111-117 https://doi.org/10.1002/(SICI)1097-0118(199710)26:2<111::AID-JGT6>3.0.CO;2-V