When dealing with garbage collection schemes, it's often helpful to think of the reference graph, which is a directed graph where the vertices are objects and there is an edge from an object A to an object B if A holds a reference to B.

When the number of vertices in the graph is known ahead of time, and additional data structures are used to determine which vertices have already been added to the queue, the space complexity can be expressed as where is the cardinality of the set of vertices.

When one considers light-cone quantized superstrings, the discussion is more subtle as divergences can arise when the light-cone vertices collide.

When spoken about graph labeling with unique labels, commonly taken from the integer range 1 ,..., n, where n is the number of the vertices of the graph, two labeled graphs are said to be isomorphic if the corresponding underlying unlabeled graphs are isomorphic.

When used without any qualification, a total coloring is always assumed to be proper in the sense that no adjacent vertices, no adjacent edges, and no edge and its endvertices are assigned the same color.

When the order of the graph G is not divisible by k, we add isolated vertices to G just enough to make the order of the new graph G ′ divisible by k.

When this splitting process has been performed for all vertices, the sequence of sets has one vertex per set, in the reverse of a perfect elimination ordering.

When a graph has a 2-join, it may be decomposed into induced subgraphs called " blocks ", by replacing one of the two subsets of vertices by a shortest path within that subset that connects one of the two complete bipartite graphs to the other ; when no such path exists, the block is formed instead by replacing one of the two subsets of vertices by two vertices, one for each complete bipartite subgraph.

When the coordinates are not negative, the point lies in the convex hull of, that is, in the simplex which has those points as its vertices.

When it exists, a circumscribed sphere need not be the smallest sphere containing the polyhedron ; for instance, the tetrahedron formed by a vertex of a cube and its three neighbors has the same circumsphere as the cube itself, but can be contained within a smaller sphere having the three neighboring vertices on its equator.

When specifically dealing with network graphs, oftentimes graphs are without loops or multiple edges to maintain simple relationships ( where edges represent connections between two people or vertices ).

When applied repeatedly, Ptolemy's theorem allows one to compute the lengths of all diagonals for polygons inscribed in a circle with vertices P < sub > 1 </ sub >, ..., P < sub > n </ sub >, if the sides are given together with all the length values of the " next to sides " chords connecting two vertices P < sub > i </ sub > and P < sub > i + 2 </ sub >

When the graph is uniformly random except for the degree distribution, these critical vertices are the ones with the highest degree, and have thus been implicated in the spread of disease ( natural and artificial ) in social and communication networks, and in the spread of fads ( both of which are modeled by a percolation or branching process ).

When a group of vertices ( normally 3, to form a triangle ) come through the vertex shader, their output position is interpolated to form pixels within its area ; this process is known as rasterisation.

When a notion of equality is properly defined, as done below, the operation of taking the dual of a hypergraph is an involution, i. e.,

When the edges of a hypergraph are explicitly labeled, one has the additional notion of strong isomorphism.

When I show up he will know you are a good wife to have told him about it ''.

When the Know-nothings get control, it will read, All men are created equal except Negroes and foreigners and Catholics.

When the reactionary response is thus bolstered by an intellectual defense, the characteristics of that defense are explicable only in terms of the basic attitudes of unanalyzed reaction.

When combined with the metaphysical notion that pure forms of this universe are best appreciated when least embodied in a material substratum, it becomes clear that while earth will be dross on a scale of material-formal ratios, celestial bodies will be of a subtle, quickened, ethereal existence, in whose embodiment pure form will be the dominant component and matter will be absent or remain subsidiary.

She used to tell me, `` When I stand there and look at the flag blowing this way and that way, I have the wonderful, safe feeling that Americans are protected no matter which way the wind blows ''.

When we consider the disorganized state of the world community, and the legacy of predispositions adversely directed against all who are identified as Jews, it is obvious that the struggle for the minds and muscles of men needs to be prosecuted with increasing vigor and skill.

When these fields are surveyed together, important patterns of relationship emerge indicating a vast community of reciprocal influence, a continuity of thought and expression including many traditions, primarily literary, religious, and philosophical, but frequently including contact with the fine arts and even, to some extent, with science.

When different colors are used, she is just as likely to color trees purple, hair green, etc..

When finally the two bedraggled men reach their friend's home, Voltaire's fears are once again aroused.

`` When are you to leave ''??

When the roof blocks are all in place, the final rows of wall blocks are mortared into position.

When the aid operations are reorganized the Peace Corps should remain a semi-autonomous, functional unit.

When the budget goes to trustees for approval it is the president's budget, to which his faith and credit are committed ; ;

When they have 4 to 6 leaves and are thrifty little plants, it's time to set them out where they are to remain.

When aircraft are no longer helpless on airfields, they are no longer vulnerable to Aj.

When more than two figures are separated by subtraction symbols the subtraction must be carried out from the left to right if the result is to be correct.

When they're on, the top edges are planed even with the sheer batten.

When painting, Mason's physical eyes are half-closed, while his mind's eye is wide open, and this circumstance accounts in part for the impression he wishes to convey.

When improvements are recommended in working conditions -- such as lighting, rest rooms, eating facilities, air-conditioning -- do you try to set a measure of their effectiveness on productivity??

When sufficiently accurate and complete measurements are available, it will be possible to set limits on the thermal and electrical characteristics of the surface and subsurface materials of the moon.

When some thirteen records of newly and recently born individuals are collated, little or no correlation between length and distribution can be detected.

When three dice are tossed repeatedly, what is the probability that the number of aces is 0 ( or 1, or 2, or 3 )??

When the topological space is homeomorphic to a simplicial complex, its fundamental group can be described explicitly in terms of generators and relations.

When referring to disk storage capacities it usually means 10 < sup > 9 </ sup > bytes, often stated explicitly on the manufacturer's permanent sticker.

When originally serialised in a magazine it was subtitled, " An Experiment in Prophecy ", and is considered his most explicitly futuristic work.

When defining the dogma in Ineffabilis Deus, Pope Pius IX explicitly affirmed that Mary was redeemed in a manner more sublime.

When Shoghi Effendi died in 1957, he died without explicitly appointing a successor Guardian, and Remey was among the nine Hands of the Cause elected as an interim authority until the election of the first Universal House of Justice in 1963.

When Hawaii was admitted to the United States in 1959, Palmyra was explicitly separated from the new state as a federal incorporated territory, administered by the U. S. Department of the Interior.

When an axiomatic system begins with its axioms, the primitive notions may not be explicitly stated.

The United States Constitution does not explicitly establish the office of Chief Justice, but presupposes its existence with a single reference in Article I, Section 3, Clause 6: " When the President of the United States is tried, the Chief Justice shall preside.

When a " destination operand " explicitly specifies the destination, the number of operand specifiers in an instruction is larger than the arity of the operation.

He does not explicitly acknowledge any anticipation of his demonstration of electrostatic repulsion by the latter but, as he quotes a passage from the same page, could not have been unaware that, in a discussion of the nature of electrical attraction, Cabeo had written ( Philosophia Magnetica p. 192 ): " When we see that small bodies ( corpuscula ) are lifted ( sublevari et attolli ) above the amber and also fall back to the motionless amber, it cannot be said that such erratic behaviour ( talem matum-but if " matum " is taken as a misprint for " motum ", then the translation is simply " such motion ") is an attraction by the gravity of the attracting body.

When dealing with functions of multiple variables, some of these variables may be related to each other, and it may be necessary to specify explicitly which variables are being held constant.

When the Basic Law is amended, this has to be done explicitly ; the concerning article must be cited.

When she drifts off to sleep, he gets a pillow and smothers her to death, although this is not explicitly shown.

When priests began to hear confessions, they responded to criticisms by pointing to the fact that such is explicitly sanctioned in The Order for the Visitation of the Sick in the Book of Common Prayer, which contains the following direction:

During his trial in 2006 before the Court of Appeal, a former head of the foreign intelligence service explicitly stated that " When special services are unable to undertake certain kinds of undercover operation, they use parallel structures.

When intangible assets and goodwill are explicitly excluded, the metric is often specified to be " tangible book value ".

When interpreted using original intent or original meaning, it clearly protects rights which the founders had not thought to list explicitly — this could be interpreted as a direct rebuke to all Textualist or Formalist legal schools including originalism.

When the functions f < sub > i </ sub > are solutions of a linear differential equation, the Wronskian can be found explicitly using Abel's identity, even if the functions f < sub > i </ sub > are not known explicitly.

When subjects were explicitly told to avoid relying on introspection, their assessments of their own bias became more realistic.

When that did not occur ( though the program thanked Van Doren explicitly, among other credits ), Van Doren wrote, Krainin later sought his cooperation and consultation when Robert Redford was beginning to make Quiz Show — even conveying that Van Doren would be paid in six figures for it.

When executed, the computer generates an integer value of 13, but because the program has not explicitly designated where in the computer this 13 is stored, the expression is an rvalue.

On the Protestant side, the Lutheran Church Missouri Synod explicitly states “ When Christ returns, “ new heavens and a new earth ” will be created ( 2 Pet.