Graphs, Matrices, and DesignsExamines partitions and covers of graphs and digraphs, latin squares, pairwise balanced designs with prescribed block sizes, ranks and permanents, extremal graph theory, Hadamard matrices and graph factorizations. This book is designed to be of interest to applied mathematicians, computer scientists and communications researchers. |
Contents
1 Around a Formula for the Rank of a Matrix Product with Some Statistical Applications | 1 |
2 Linear Operators Preserving Partition Numbers of Graphs | 19 |
A Generalization of Sterns Theorem | 31 |
4 Completion of the Spectrum of Orthogonal Diagonal Latin Squares | 43 |
5 Deficiencies and Vertex Clique Covering Numbers of Cubic Graphs | 51 |
6 Extremal Problems for the BondyChvatal Closure of a Graph | 73 |
7 The 3Hypergraphical Steiner Quadruple Systems of Order Twenty | 85 |
8 Minimum Biclique Partitions of the Complete Multigraph and Related Designs | 93 |
12 Pairwise Balanced Designs with Holes | 171 |
13 The Sum Number of Complete Bipartite Graphs | 205 |
14 Biclique Covers and Partitions of Unipathic Digraphs | 213 |
15 Maximal Partial Latin Squares | 225 |
16 Longest Cycles in 3Connected Graphs of Bounded Maximum Degree | 237 |
17 Construction of New Hadamard Matrices with Maximal Excess and Infinitely Many New SBIBD 4ksup2 2ksup2+k ksup2+k | 255 |
18 Maximum Order Digraphs for Diameter 2 or Degree 2 | 269 |
19 Minimal Clique Partitions of Norm Three II | 279 |
9 Multiplicativity of Generalized Permanents over Semirings | 121 |
10 A Few More Room Frames | 133 |
11 Pairwise Balanced Designs with Block Sizes 5t + 1 | 147 |
20 The Cycle Space of an Embedded Graph III | 295 |
Some General Questions | 299 |
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Common terms and phrases
1-factors 3-connected 4.7 Rees Theorem adjacency matrix Algebra Applications B₁ bicliques cleavage unit clique covering clique partition number Combinatorial complete bipartite graph complete graph conference matrix construction contains Corollary 4.7 Rees cycle d-semigroup decomposition def G define deleting denote diagonal Discrete Math disjoint edge-graph elements empty cell exact partition exists a PBDH(n F₁ factorizable factors frame of type G₁ graph G graph of order Graph Theory GV Km Hadamard matrices Hence hill-climbing algorithm incidence matrix independent set k-regular Latin squares Lemma Let G Linear Algebra Mathematics matrix of order maximal excess maximum minimal clique partition Moore graph Multilinear Algebra nonzero norm three bound obtain one-factorization orthogonal P₁ pair parallel classes permutation points proof of Theorem Pullman regular graphs result semiring sequences subgraph subset Suppose T₁ Table transversal triangles triple system TS(v TS(w v₁ vertex vertices