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 |
Completion of the Spectrum of Orthogonal Diagonal Latin Squares | 43 |
Extremal Problems for the BondyChvátal Closure of a Graph | 73 |
Furino Department of Mathematics St Jeromes College Waterloo Ontario | 92 |
Minimum Biclique Partitions of the Complete Multigraph | 93 |
Multiplicativity of Generalized Permanents over Semirings | 121 |
Pairwise Balanced Designs with Block Sizes 5t + 1 | 147 |
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 |
The Cycle Space of an Embedded Graph III | 295 |
Pairwise Balanced Designs with Holes | 171 |
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Common terms and phrases
1-factors 3-connected 4.7 Rees Theorem adjacency matrix Applications 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 K₂ Latin squares Lemma Let G matrix of order maximal excess maximum minimal clique partition Moore graph Multilinear Algebra nonzero norm three bound obtain one-factors orthogonal P₁ pair pairwise balanced designs parallel classes PBDH(n+s:s permutation points proof of Theorem Pullman regular graphs result row and column semiring sequences strong unipathic digraph strongly preserves Styan subgraph subset Suppose Table transversal triangles triple system TS(v TS(w v₁ vertex