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Daphne Der-Fen Liu

Professor
Department of Mathematics
College of Natural and Social Sciences

Office: Simpson Tower F201
Phone: (323) 343-2161
FAX: (323) 343-5071
Email: dliu@calstatela.edu

Ever since joined the Cal State LA faculty in 1991, I have been pursuing both my research and teaching goals.  In 2003, I received a CSULA Outstanding Professor Award.  Currently my research is partly supported by the NSF (National Science Foundation) under a grant entitled “Graph Coloring Parameters: Their Interplay with Number Theory Problems and Applications to Broadcast Communications” (2003-2006). I am also grateful to another NSF research grant awarded to me during 1998 – 2001. 

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glasses.gif (111 bytes)Research Interests

There are two major parts in my research: The first part is about graph coloring parameters (including fractional chromatic number and circular chromatic number) of distance graphs and their relations to some number theory problems such as the "density of integral sets with missing differences" and the so called "lonely runner conjecture."

The other part of my research includes various generalized coloring problems motivated by the "channel assignment problem" introduced by Hale in 1980.  The problems I have been working on include T-coloring, no-hole T-coloring, distance two labeling, circular distance two labeling, and the generalized distance labeling.    

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wpec.jpg (22775 bytes)Publications

 

1.      D. Liu, T-colorings of Graphs, Discrete Mathematics, 101 (1992), 203 – 211.

2.      D. Liu, On a Conjecture of T-colorings, Congressus Numerantium, 103 (1994), 27 – 31.

3.      J. Griggs and D. Liu, Channel Assignment Problem for Mutually Adjacent Sites, J. Combinatorial Theory Series A, 68 (1994), 169 – 183.

4.      D. Liu, T-Graphs and the Channel Assignment Problem, Discrete Mathematics, 161 (1996), 197 – 205.

5.      D. Liu and R. Yeh, On Distance Two Labellings of Graphs, Ars Combinatoria, 47 (1997), 13 – 22.

6.      D. Liu and R. Yeh, No-hole T-coloring of Graphs [dvi] [pdf], Congressus Numerantium, 138 (1999), 39 – 48.

7.      K.-W. Lih, D. Liu and X. Zhu, Star-Extremal Circulant Graphs [dvi] [pdf], SIAM J. Discrete Mathematics, 12 (1999), 491 – 499.

8.      D. Liu and X. Zhu, Distance Graphs with Missing Multiples in the Distance Sets [dvi] [pdf], J. Graph Theory, 30 (1999), 245 – 259.

9.      G. J. Chang, D. Liu and X. Zhu, Distance Graphs and T-coloring [dvi] [pdf], J. Combinatorial Theory Series B, 75 (1999), 259 -269.

10.  G. J. Chang, W. Ke, D. Kuo, D. Liu and R. Yeh, On L(d,1)-Labelings of Graphs [dvi] [pdf], Discrete Mathematics, 220 (2000), 57-66.

11.  D. Liu, Chromatic Number of Distance Graphs and the Channel Assignment Problem [dvi] [pdf], Ars Combinatoria, 56 (2000), 65–80.

12.  G. J. Chang, S. Juan and D. Liu, Minimum Span of No-hole (r+1)-Distant Coloring [dvi] [pdf], SIAM J. Discrete Mathematics, 14 (2001), 370 – 380.

13.  D. Liu, Relating Hamiltonicity and Path Covering to Distance Two Labellings of  Graphs [dvi] [pdf], Discrete Mathematics, 232 (2001), 163 – 169.

14.  G. J. Chang, S. Juan and D. Liu, No-Hole 2-Distant Coloring for Unit Interval Graphs [dvi] [pdf], Ars Combinatoria, 61 (2001), 233–244.

15.  K.-W. Lih and D. Liu, Circular Chromatic Number of some Reduced Kneser Graphs [dvi] [pdf], J. Graph Theory, 41 (2002), 62–68.

16.  D. Liu and X. Zhu, Asymptotic Clique Covering Ratio of Distance Graphs [dvi] [pdf], European J. of Combinatorics, 23 (2002), 315 – 327.

17.  D. Liu and X. Zhu, Circular Distance Two Labelings and Circular Chromatic Numbers [dvi] [pdf], Ars Combinatoria, 69 (2003), 177 – 183.

18.  D. Liu, On sizes of Graphs with Fixed Orders and Spans of Circular Distance Two Labellings [dvi] [pdf], Ars Combinatoria, 67 (2003), 125 – 139.

19.  D. Liu, Circular Chromatic Number of Iterated Mysielski Graphs [dvi] [pdf], Discrete Mathematics, 285 (2004), 335 – 334.

20.  D. Liu and M. Xie, Radio Number for Square of Cycles [pdf], Congressus Numerantium, 169 (2004), 105 – 125.

21.  D. Liu and X. Zhu, Fractional Chromatic Number and Circular Chromatic Number for Distance Graphs with Large Clique Size [dvi] [.pdf], Journal of Graph Theory, 47 (2004), 129 – 146. Erratum [pdf], J. of Graph Theory, 48 (2005), 329 – 330.

22.  D. Liu and X. Zhu, The Circular Distance Two Labeling and the L(2, 1)-Number for Outerplanar Graphs [pdf] SIAM J. Discrete Mathematics, 19 (2005), 281 – 293.

23.  D. Liu and X. Zhu, Multi-level distance labelings and radio number for paths and cycles [pdf], SIAM J. Discrete Mathematics, 19 (2005), 610 – 621.

24.  D. Liu and M. Xie, Radio Number for Square Paths [pdf], Ars Combinatoria, to appear.

25.  K-W. Lih and D. Liu, Pascal's Labeling and Path Counting [pdf], manuscript, 2004.

26.  D. Liu, Circular Coloring for Graphs with Distance Constraints [dvi], manuscript, 2005.                 

27.  D. Liu and X. Zhu, Coloring the Cartesian Sum of Graphs [pdf], manuscript, 2005.

28.  D. Liu and X. Zhu, Fractional Chromatic Number of Distance Graphs with Two Interval Distance Sets [pdf], manuscript, 2005.  

29.  D. Liu, Radio Number for Trees [pdf], manuscript, 2006.

30.  D. Liu, Hamiltonian Spectrum for Trees [pdf], manuscript, 2006.

31.  R. Justie and D. Liu, Antipodal Labeling for Cycles [pdf], manuscript, 2006.

 

wpeD.jpg (18527 bytes)Teaching Interests and Experiences

In the past years at Cal State LA, I have taught more than twenty different mathematics subjects ranging from general education math to graduate courses. I enjoyed very much teaching most of them, especially, graph theory, modern algebra, linear algebra, discrete mathematics, linear programming, theory of probability, matrix theory, and calculus I - IV, etc.

With a CSULA Innovative Teaching Award, I have created a senior/graduate course Math 484 Graph Theory, which is offered every year since 1999. 

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datebook.gif (548 bytes)Schedule for Fall 2006:

 

 Courses:

 

·        Math 102: College Algebra                  TTH 9:50 – 11:30 

·        Math 474: Theory of Probability         TTH 1:30 – 3:10

 

 Office Hours: TTH 9:30 – 9:50 AM; 11:30 – Noon and  1 – 1:30 PM.

 

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hut.gif (1077 bytes)Education   

Ph. D. Mathematics, University of South Carolina, Columbia, June 1991.
Dissertation: "Graph Homomorphism and the Channel Assignment Problem". Advisor: Jerrold R. Griggs.            

 

B.S. Mathematics, National Central University, Taiwan, June 1985.

 

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Family photos: [Four of us at Bryce Canyon] [Four of us in Taiwan] [Jessica & Anthony] [J & A & D bicycling]

verity.gif (1996 bytes)Interesting Links 

Graph Theory Resources

Chinese Daily News

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This page was last updated on 02/15/200609/25/02.