Title: Number 7 Discrete Mathematics Author: R.Balakrishnan C.E.Veni Madhavan |

**Table of Contents**

- List-colorings and the Number of Colorings of a Graph, Carsten Thomassen 1

- Homomorphisms, Dualities and CSP, Jaroslav Neˇsetˇril 9

- Introduction to the Minimum Cost Homomorphism Problem for Directed and Undirected Graphs, Gregory Gutin 25

- Refinements of Ramanujan’s Congruence Modulo 5, Herbert S. Wilf 39

- Almost Ramsey Type Theorems for Directed Graphs, S.B. Rao and Sushmita Ruj 43

- Some Recent Results on Domination in Graphs(An Extended Abstract), M.D. Plummer 55

- Resistance Matrix and q-Laplacian of a Unicyclic Graph, R.B. Bapat 63

- A Discussion of Constrained Binary Embeddings withApplications to Cryptanalysis of Irregularly Clocked StreamCiphers, Diane M. Donovan, James Lefevre and Leonie Simpson 73

- Disjoint Dominating Sets in Graphs, Sandra M. Hedetniemi, Stephen T. Hedetniemi, Renu C. Laskar,Lisa Markus and Peter J. Slater 87

- On the Complexity of the Geodetic and Convexity Numbersof a Graph, Mitre C. Dourado, F´abio Protti and J. L. Szwarcfiter 101

- Non-binary Codes via the Trace Map, Asha Rao and N. Pinnawalai 109

- Vertex Identifying Codes for Fault Isolation in Communication Networks, Krishnaiyan Thulasiraman, Min Xu, Ying Xiao and Xiao-Dong Hu 115

- On the Berge’s k-Optimal Path Partition Conjecture, Sriraman Sridharan 125

- Circular Perfect Graphs, Xuding Zhu 131

- Generalized Colourings and Matrix Partitions, Pavol Hell 141

- Applications of Orthogonal Arrays to Computer Science, K. Gopalakrishnan and Douglas R. Stinson 149

- Forbidden Intersection Patterns in the Families of Subsets, Gyula O.H. Katona 165

- Directed Odd Cycle Decompositions of Some RegularDigraphs, R.S. Manikandan, P. Paulraja and S. Sivasankar 175

- Packing and Domination Invariants on Cartesian Products andDirect Products, Douglas F. Rall 183

- Independent Domination and Graph Colorings, S. Arumugam, I. Sahul Hamid and A. Muthukamatchi 195

- Graph Equivalences and Decompositions Definable in MonadicSecond-Order Logic. The Case of Circle Graphs, Bruno Courcelle 205

- Restrained Domination in Graphs, Johannes H. Hattingh 217

- Some Properties of the Clique Graph of a Cograph, S. Aparna Lakshmanan and A.VijayakumariiContents 227

- ˆ Sk Sk-Factorization of Symmetric Digraph of Tensor Product of Graphs, P. Hemalatha and A. Muthusamy 233

- Some New Degree Concepts in Graphs, S.S. Kamath and R.S. Bhat 237

- The Edge C4 Graph of a Graph, Manju K. Menon and A.Vijayakumar 245

- Topological Properties of the Set of All Minimal Dominating Functions of Graphs, K. Reji Kumar 249

- γt-Graph of a Graph G, S. Amutha and N. Sridharan 255

- Some Combinatorial Results on Pcodes, K. Sasikala, V.R. Dare and D.G. Thomas 263

- Characterizing Defect 1-Extendable Bipartite Graphs and an Algorithm, Xuelian Wen and Dingjun Lou 271