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Daphne Der-Fen Liu


Professor and Graduate Advisor
Department of Mathematics
College of Natural and Social

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. I have received a CSULA Outstanding Professor Award, 2003. I have worked on and am grateful for two National Science Foundation research grants: Graph Coloring Parameters: Their Interplay with Number Theory Problems and Applications to Broadcast Communications (2003-2007) and a POWRE (Professional Opportunity for Women in Research and Education) award 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, Graph homomorphism and the channel assignment problem, Ph.D. Dissertation, University of South Carolina, Columbia, 1991.

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

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

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

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

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

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

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

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

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

11.  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.

12.  D. Liu, Chromatic Number of Distance Graphs and the Channel Assignment Problem [dvi] [pdf], Ars Combinatoria, 56 (2000), 6580.

13.  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.

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

15.  G. J. Chang, S. Juan and D. Liu, No-Hole 2-Distant Coloring for Unit Interval Graphs [dvi] [pdf], Ars Combinatoria, 61 (2001), 233244.

16.  K.-W. Lih and D. Liu, Circular Chromatic Number of some Reduced Kneser Graphs [dvi] [pdf], J. Graph Theory, 41 (2002), 6268.

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

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

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

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

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

22.  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.

23.  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.

24.  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.

25.  D. Liu and X. Zhu, Coloring the Cartesian Sum of Graphs [pdf], Disc. Math., 308 (2008), 5928 -- 5936.

26.  D. Liu and X. Zhu, Fractional Chromatic Number of Distance Graphs with Two Interval Distance Sets [pdf], European J. Combinatorics, 29 (2008), 1733 1743.

27.  D. Liu, Radio Number for Trees [pdf], Disc. Math., 308 (2008), 1153 1164.

28.  D. Liu, From Rainbow to the Lonely Runner: A Survey [pdf], Taiwanese J. Math., 12 (2008), 851 871.

29.  D. Liu and M. Xie, Radio Number for Square Paths [pdf], Ars Combinatoria, 90 (2009), 307 319.

30.  K.-W. Lih, D. Liu and W.-F. Wang, On (d,1)-total numbers of graphs, Discrete Mathematics, 309 (2009), 3767 3773.

31.  W. Lin, D. Liu and X. Zhu, Multi-colouring the Mycielskian of graphs, Journal of Graph Theory, 63 (2010), 311 323.

32.  D. Liu, Hamiltonian Spectrum for Trees [pdf], Ars Combinatoria, to appear.

33.  J. Juan and D. Liu, Antipodal Labeling for Cycles [pdf], Ars Combinatoria, to appear.

34.  J. Juan, D. Liu and L. Chen, L(j, k)-Labelling for trees, Discrete Applied Mathematics, 158 (2010), 692 698.


35.  D. Liu, Norine, Pan, and Zhu, Circular Consecutive Choosibility for k-Choosable Graphs, Journal of Graph Theory, in production, 2010.

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

37.  D. Liu, Circular Coloring for Graphs with Distance Constraints [dvi], manuscript, 2007.                 


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.

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datebook.gif (548 bytes)Schedule for Fall 2010:



        Math 248: Discrete Math TuTh 11:40 1:20

        Math 474: Theory of Probability TuTh 9:50 11:30

Office Hours: TuTh 2 4:30 pm; W: 1:30 3:30 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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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.