Discrete Mathematics..

Index 733Dijkstra’s algorithm, 600–2Dimension of a matrix, 285–6Direct product, external, 372Direct proof, 51–4, 56Directed cycle in a digraph, 541Directed edge sequence in adigraph, 541Directed graph of a relation, seeDigraph of a relationDirected graph, see DigraphDirected path in a digraph, 541Disjoint, pairwise, 113Disjoint sets, 88Disjunction, 5–6exclusive, 6inclusive, 5Disjunctive normal form, 448Distancebetween binary words, 414minimum, of a code, 417–18,419Distributive lawsfor matrices, 300for propositions, 21for sets, 99Divisibility relation, 171, 183, 187,189, 192–3, 197Dodecahedral graph, 508–9Dodecahedron, 508Domain of a function, 218, 255Dualof a Boolean algebra statement,435–6of a proposition, 22of a set theoretic statement, 101Duality principlefor a Boolean algebra, 436for propositions, 23for sets, 101–2Edge(s) of a graph, 488adjacent, 491Edge sequencedirected, in a digraph, 541in a graph, 501Element(s)greatest, 185idempotent, 371identity, 359, 361in a Boolean algebra, 432image of, 218, 222, 240inverse of, 359, 361least, 185–6maximal, 186minimal, 186of a matrix, 285of a set, 73order of, 394–5, 403–4powers of, 374, 378–9self-inverse, 360Elementary column operation,302–7Elementary column transformation,see Elementary columnoperationElementary matrix, 302–11inverse of, 314–15post-multiplication by, 306–10pre-multiplication by, 304–10,316Elementary row operation, 302–11,314–22, 340–54inverse of, 314–15Elementary row transformation, seeElementary row operationEliminationGauss–Jordan, 336–49Gaussian, 349–53Empty relation, 163Empty set, 75, 79, 134, 142power set of, 110Empty string, 367Encoding function, 415Entry of a matrix, see Element of amatrixEnumeration theory, see CountingtechniquesEpimorphism, 406