The L(2, 1)-Labeling Problem via the Semi-Tensor Product Method

This paper investigates the L(2, 1)-labeling problem, and presents a number of new results and algorithms. First, the distance problem is considered, and a necessary and sufficient condition is presented. Second, using semi-tensor product, two sufficient and necessary conditions for the solvability of the L(2, 1)-labeling problem are obtained, based on which a new algorithm is designed to find all the feasible L(2, 1)-labeling schemes for any simple graph. Finally, study of one illustrative example is shown the effectiveness of the results/algorithms presented in this paper.

[1]  P. Steerenberg,et al.  Targeting pathophysiological rhythms: prednisone chronotherapy shows sustained efficacy in rheumatoid arthritis. , 2010, Annals of the rheumatic diseases.

[2]  M. Margaliot.  Controllability and observability of Boolean control networks , 2012 .

[3]  Daizhan Cheng,et al.  Disturbance Decoupling of Boolean Control Networks , 2011, IEEE Transactions on Automatic Control.

[4]  Qiaoling Ma,et al.  The (2,1) -Total Labeling of Double Graph of Some Graphs , 2011 .

[5]  Yuzhen Wang,et al.  A matrix approach to graph maximum stable set and coloring problems with application to multi-agent systems , 2012, Autom..

[6]  Yuzhen Wang,et al.  Robust graph coloring based on the matrix semi-tensor product with application to examination timetabling , 2014 .

[7]  Yuzhen Wang,et al.  Algebraic formulation and strategy optimization for a class of evolutionary networked games via semi-tensor product method , 2013, Autom..

[8]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[9]  Daizhan Cheng,et al.  Realization of Boolean control networks , 2010, Autom..

[10]  Roger K. Yeh.  A survey on labeling graphs with a condition at distance two , 2006, Discret. Math..

[11]  Wei-Fan Wang,et al.  (2, 1)-Total labelling of outerplanar graphs , 2007, Discret. Appl. Math..

[12]  Daizhan Cheng,et al.  Analysis and Control of Boolean Networks , 2011 .

[13]  Fangfei Li,et al.  Controllability of Boolean control networks with time delays in states , 2011, Autom..

[14]  G. Chang,et al.  Labeling graphs with a condition at distance two , 2005 .

[15]  Sarah Spence Adams,et al.  The minimum span of L(2, 1)-labelings of certain generalized Petersen graphs , 2007, Discret. Appl. Math..

[16]  Gerard J. Chang,et al.  The L(2, 1)-Labeling Problem on Graphs , 1996, SIAM J. Discret. Math..

[17]  D. Cheng,et al.  Stability and stabilization of Boolean networks , 2011 .

[18]  Yuzhen Wang,et al.  Boolean derivative calculation with application to fault detection of combinational circuits via the semi-tensor product method , 2012, Autom..

[19]  Daizhan Cheng,et al.  A Linear Representation of Dynamics of Boolean Networks , 2010, IEEE Transactions on Automatic Control.

[20]  Meirong Xu,et al.  T-coloring of graphs with application to frequency assignment in cellular mobile networks , 2014, CCC 2014.

[21]  Jerrold R. Griggs,et al.  Labelling Graphs with a Condition at Distance 2 , 1992, SIAM J. Discret. Math..

[22]  D. Cheng,et al.  Semi-tensor Product of Matrices , 2011 .