L(2, 1)-labelling of Circular-arc Graph

An L(2,1)-labelling of a graph $G=(V, E)$ is $\lambda_{2,1}(G)$ a function $f$ from the vertex set V (G) to the set of non-negative integers such that adjacent vertices get numbers at least two apart, and vertices at distance two get distinct numbers. The L(2,1)-labelling number denoted by $\lambda_{2,1}(G)$ of $G$ is the minimum range of labels over all such labelling. In this article, it is shown that, for a circular-arc graph $G$, the upper bound of $\lambda_{2,1}(G)$ is $\Delta+3\omega$, where $\Delta$ and $\omega$ represents the maximum degree of the vertices and size of maximum clique respectively.

[1]  Madhumangal Pal,et al.  Maximum weight independent set of circular-arc graph and its application , 2006 .

[2]  Daniel Král,et al.  A Theorem about the Channel Assignment Problem , 2003, SIAM J. Discret. Math..

[3]  Madhumangal Pal,et al.  An Optimal Algorithm for Solving All-Pairs Shortest Paths on Trapezoid Graphs , 2002, Int. J. Comput. Eng. Sci..

[4]  Madhumangal Pal,et al.  Selection of programme slots of television channels for giving advertisement: A graph theoretic approach , 2007, Inf. Sci..

[5]  Madhumangal Pal,et al.  Maximum weight k-independent set problem on permutation graphs , 2003, Int. J. Comput. Math..

[6]  Madhumangal Pal,et al.  An efficient algorithm to generate all maximal independent sets on trapezoid graphs , 1999, Int. J. Comput. Math..

[7]  M. Pal,et al.  A Sequential Algorithm to Solve Next-to-Shortest Path Problem on Circular-arc Graphs , 2006 .

[8]  Tiziana Calamoneri,et al.  Optimal L(h, k)-Labeling of Regular Grids , 2006, Discret. Math. Theor. Comput. Sci..

[9]  Bhawani Sankar Panda,et al.  L(2,1)-labeling of dually chordal graphs and strongly orderable graphs , 2012, Inf. Process. Lett..

[10]  Madhumangal Pal,et al.  An efficient pram algorithm for maximum-weight independent set on permutation graphs , 2005 .

[11]  Madhumangal Pal,et al.  An optimal parallel algorithm for solving all-pairs shortest paths problem on circular-arc graphs , 2005 .

[12]  Alan A. Bertossi,et al.  Approximate L(δ 1 ,δ 2 ,…,δ t )-coloring of trees and interval graphs , 2007 .

[13]  Madhumangal Pal,et al.  An Efficient Algorithm for Finding a Maximum Weight k-Independent Set on Trapezoid Graphs , 2001, Comput. Optim. Appl..

[14]  Toru Araki,et al.  Labeling bipartite permutation graphs with a condition at distance two , 2009, Discret. Appl. Math..

[15]  Madhumangal Pal,et al.  An Optimal Algorithm to Find Maximum and Minimum Height Spanning Trees on Cactus Graphs , 2008 .

[16]  Madhumangal Pal,et al.  An Efficient Algorithm for Finding All Hinge Vertices on Trapezoid Graphs , 2002, Theory of Computing Systems.

[17]  Jan van Leeuwen,et al.  Approximations for lambda-Colorings of Graphs , 2004, Comput. J..

[18]  Stephan Olariu,et al.  On the L(h, k)-labeling of co-comparability graphs and circular-arc graphs , 2009 .

[19]  Frank Harary,et al.  A Radio Coloring of a Hypercube , 2002, Int. J. Comput. Math..

[20]  Lorna Stewart,et al.  A Linear Recognition Algorithm for Cographs , 1985, SIAM J. Comput..

[21]  Madhumangal Pal,et al.  (2,1)-Total Labelling of Cactus Graphs , 2010 .

[22]  Madhumangal Pal,et al.  ( 2 , 1 ) L Labelling of Cactus Graphs , 2012 .

[23]  Hirotaka Ono,et al.  A Linear Time Algorithm for L(2, 1)-Labeling of Trees , 2009, ESA.

[24]  Denise Sakai,et al.  Labeling Chordal Graphs: Distance Two Condition , 1994 .

[25]  Madhumangal Pal,et al.  An Optimal Algorithm to Solve 2-Neighbourhood Covering Problem on Interval Graphs , 2002, Int. J. Comput. Math..

[26]  Márcia R. Cerioli,et al.  On L(2, 1)-coloring split, chordal bipartite, and weakly chordal graphs , 2012, Discret. Appl. Math..

[27]  W. K. Hale.  Frequency assignment: Theory and applications , 1980, Proceedings of the IEEE.

[28]  Madhumangal Pal,et al.  Labelling of Cactus Graphs , 2012 .

[29]  Tiziana Calamoneri,et al.  The L(h, k)-Labelling Problem: An Updated Survey and Annotated Bibliography , 2011, Comput. J..

[30]  Madhumangal Pal,et al.  L(0, 1)-Labelling of Cactus Graphs , 2012 .

[31]  Madhumangal Pal,et al.  Optimal sequential and parallel algorithms for computing the diameter and the center of an interval graph , 1995, Int. J. Comput. Math..

[32]  Madhumangal Pal.  Efficient algorithms to compute all articulation points of a permutation graph , 1998 .

[33]  Flavia Bonomo,et al.  On the L(2, 1)-labelling of block graphs , 2011, Int. J. Comput. Math..

[34]  Alan A. Bertossi,et al.  Efficient use of radio spectrum in wireless networks with channel separation between close stations , 2000, DIALM '00.

[35]  Madhumangal Pal,et al.  The Parallel Algorithms for Determining Edge-packing and Efficient Edge Dominating Sets in Interval Graphs , 1995, Parallel Algorithms Appl..

[36]  Madhumangal Pal,et al.  An Optimal Algorithm to Solve the All-Pairs Shortest Paths Problem on Permutation Graphs , 2003, J. Math. Model. Algorithms.

[37]  Madhumangal Pal,et al.  An Optimal Parallel Algorithm to Color an Interval Graph , 1996, Parallel Process. Lett..

[38]  Madhumangal Pal,et al.  An optimal parallel algorithm for computing cut vertices and blocks on interval graphs , 2000, Int. J. Comput. Math..

[39]  Madhumangal Pal,et al.  An Efficient Algorithm to Generate all Maximal Cliques on Trapezoid Graphs , 2002, Int. J. Comput. Math..

[40]  Madhumangal Pal,et al.  An Algorithm to find a Minimum Feedback Vertex Set of an Interval Graph , 2005 .

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

[42]  Rossella Petreschi,et al.  L(h, 1)-labeling subclasses of planar graphs , 2004, J. Parallel Distributed Comput..

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