Glossary in Java Generating qr-codes in Java Glossary

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Glossary generate, create qr bidimensional barcode none for java projects datamatrix smaller ord jvm QR Code ISO/IEC18004 er A function f: N -* R has smaller order than another function g, written f -< g, if and only if f is Big Oh of g but g is not Big Oh of f. For example, n7 -< 2". p.

248 source This is a distinguished vertex in a directed network. p. 441 spanning tree A spanning tree for a connected graph G is a subgraph which is a tree and which includes every vertex of 5.

p. 378 strongly connected A digraph is strongly connected if and only if there is a walk from any vertex to any other vertex which respects orientation of arcs. p.

343 strongly connected orientation A strongly connected orientation of a graph is an assignment of orientations (directions) to all edges in such a way that the resulting digraph is strongly connected. p. 405 subgraph A subgraph of a pseudograph ! is a pseudograph whose vertices and edges are subsets of the vertices and edges, respectively, of G.

p. 287 subset A set A is a subset of a set B, denoted A C B. if and only if every element of A is also an element of B.

For example, {0, 1 C (0, 1, 2} but Z : N. p. 40 surjective Another word for onto.

p. 73 symmetric A binary relation - on a set A is symmetric if and only if a - b implies b - a. For example, a - b if and only if ab = I defines a symmetric relation on Q, but < does not.

p. 52 symmetric difference The symmetric difference of sets A and B, denoted A @ B, is the set of elements which belong to precisely one of the sets. More generally, the symmetric difference AI (d A2 a A3 E .

D A,, of n sets AI, A2 , A3 , . . , An is the set of those elements which are members of an odd number of the sets Ai.

For example, (0, 1, 2, 3} D (0, 1, 4, 5} = (2, 3, 4, 5}. pages 47 and 161..

trail A tra il in a pseudograph is a walk in which all edges are distinct. p. 303 transitive A binary relation - on a set A is transitive if and only if a - b and b - c implies a - c.

For example, the binary relation - defined by a - b if ab > 0 is a transitive relation on Z \ (0} but not on Z. p. 54 transitive tournament A transitive tournament is a tournament with the property that whenever uv and vw are.

arcs, so is uw an arc. p. 357. Traveling S qrcode for Java alesman"s Problem The Traveling Salesman"s Problem is to find a Hamiltonian cycle of least weight in a weighted connected graph. p. 325 tree A tree is a connected graph which contains no circuits.

p. 369 triangle A triangle in a graph is a 3-cycle. p.

299 U uncountable An uncountable set is an infinite set which does not have the cardinality of N. For example, the real numbers form an uncountable set. p.

90 union The union of sets-denoted A U B for two sets, A U B U C for three, and U. I A, for n-is the set of elements which belong to at least one of them. For example, 0,1,2)U{0,1,3 ={0,1,2,3}.

p.43 V valid argument See argument. value of a flow The value of a flow {fu,,1 in a directed network with source s, sink t, and vertex set V is the integer.

val(.F) =E fsvVCV f Vs;. fv p 443 equivalently, val(.F) =. E VEV fp.evV T tautology spring framework qr codes A tautology is a compound statement that is always true. For example, (pAq) -* (pvq) is a tautology. (Examine the truth table.

) p. 20 term The terms of a sequence are the numbers of its range or, thinking of a sequence as a list, the numbers in the list. For example, the first five terms of the Fibonacci sequence are 1, 1,2,3,5.

p. 164 total order A total order on a set is a partial order in which every two elements are comparable. For example, < is a total order on R, but C is not a total order on P(R).

p. 64 tournament A tournament is a digraph with the property that for every two distinct vertices u, v, exactly one of uv, vu is an arc. p.

355. walk A walk in a pseudograph is an alternating sequence of vertices and edges, beginning and ending with a vertex, in which each vertex (except the last) is incident with the edge which follows it and the last vertex is incident with the preceding edge. It is closed if and only if the first vertex is the same as the last and otherwise open. p.

303 weighted graph A weighted graph is a graph in which there is a nonnegative real number associated with each p. 325 edge. Well-Ordering Principle This principle asserts that every nonempty set of natural numbers has a smallest element.

p. 98.
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