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
Around a Formula for the Rank of a Matrix Product with Some | 1 |
Linear Operators Preserving Partition Numbers of Graphs | 19 |
A Generalization of Sterns | 31 |
Completion of the Spectrum of Orthogonal Diagonal Latin Squares | 43 |
Deficiencies and Vertex Clique Covering Numbers of Cubic Graphs | 51 |
Extremal Problems for the BondyChvátal Closure of a Graph | 73 |
The 3Hypergraphical Steiner Quadruple Systems of Order Twenty | 85 |
Furino Department of Mathematics St Jeromes College Waterloo Ontario | 92 |
Pairwise Balanced Designs with Block Sizes 5t + 1 | 147 |
Pairwise Balanced Designs with Holes | 171 |
The Sum Number of Complete Bipartite Graphs | 205 |
Kim A S Hefner Department of Mathematics United States Naval Postgraduate | 213 |
Maximal Partial Latin Squares | 225 |
Peter Horák Katedra matematiky Bratislava Czechoslovakia | 237 |
Construction of New Hadamard Matrices with Maximal Excess | 255 |
Maximum Order Digraphs for Diameter 2 or Degree 2 | 269 |
Minimum Biclique Partitions of the Complete Multigraph | 93 |
Multiplicativity of Generalized Permanents over Semirings | 121 |
The Cycle Space of an Embedded Graph III | 295 |
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Common terms and phrases
1-factors 3-connected 4.7 Rees Theorem adjacency matrix Applications B₁ bicliques cleavage unit clique covering clique partition number 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 set edge-graph elements empty cell exact partition exists a PBDH(n F₁ factors frame of type G₁ graph G Graph Theory GV Km Hadamard matrices Hence hill-climbing algorithm incidence matrix independent set K₁ Latin squares Lemma Let G matrix of order maximal excess minimal clique partition Moore graph Multilinear Algebra n₁ nonzero norm three bound obtain one-factors orthogonal P₁ pair parallel classes partition of GV permutation points proof of Theorem Pullman regular graphs result row and column semiring sequences strong unipathic digraph strongly preserves subgraph subset Suppose T₁ Table transversal triangles triple system v₁ vcc(G vertex