However, these other algorithms can also find minimum spanning forests of disconnected graphs, while Prim's algorithm requires the graph to be connected.

Regular graphs of degree at most 2 are easy to classify: A 0-regular graph consists of disconnected vertices, a 1-regular graph consists of disconnected edges, and a 2-regular graph consists of disconnected cycles and infinite chains.

For example, in graph theory, a connected graph is one from which we must remove at least one vertex to create a disconnected graph.

Similarly, a graph is 2-connected if we must remove at least two vertices from it, to create a disconnected graph.

A connected graph G with the same vertex set as a connected hypergraph H is a host graph for H if every hyperedge of H induces a connected subgraph in G. For a disconnected hypergraph H, G is a host graph if there is a bijection between the connected components of G and of H, such that each connected component G < nowiki >'</ nowiki > of G is a host of the corresponding H < nowiki >'</ nowiki >.

Additionally, the H-minor-free graphs have a separator theorem similar to the planar separator theorem for planar graphs: for any fixed H, and any n-vertex H-minor-free graph G, it is possible to find a subset of O (√ n ) vertices the removal of which splits G into two ( possibly disconnected ) subgraphs with at most 2n / 3 vertices per subgraph.

However, a graph G that has some isolated vertices, and is therefore disconnected, may nevertheless have a connected line graph.

In any graph, a vertex separator is a set of vertices the removal of which leaves the remaining graph disconnected ; a separator is minimal if it has no proper subset that is also a separator.

A skew partition is a partition of a graph's vertices into two subsets, one of which induces a disconnected subgraph and the other of which has a disconnected complement ; had conjectured that no minimal counterexample to the strong perfect graph conjecture could have a skew partition.

In the film, a survivor of a futuristic third World War is obsessed with a distant and disconnected memories of a pier at the Orly Airport, the image of a mysterious woman, and a man's death.

A more compact view of EMR is that the far-field that composes EMR is generally that part of the EM field that has traveled sufficient distance from the source, that it has become completely disconnected from any feedback to the charges and currents that were originally responsible for it.

The dramatic focus of the painting, portraying his entire family, is dispersed in a series of separate and disconnected figures of sorrow.

This is done with the pump disconnected from the body to prevent accidental insulin delivery

As the original spaces are discrete, the limit space is totally disconnected.

This group is disconnected ; it has two connected components corresponding to the positive and negative values of the determinant.

This group is disconnected, but it has a connected subgroup SO < sub > n </ sub >( R ) of the same dimension consisting of orthogonal matrices of determinant 1, called the special orthogonal group ( for n = 3, the rotation group SO ( 3 )).

The last major mounting type is one that is disconnected from humans, as part of an armament system, such as a tank coaxial or part of aircraft's armament.

Magnetic reconnection in the near-Earth magnetotail, producing a disconnected " plasmoid " One possible scenario ( the subject is still debated ) is as follows.

The product is a Boolean space ( compact, Hausdorff and totally disconnected ), and X < sub > F </ sub > is a closed subset, hence again Boolean.

Formally, a profinite group is a Hausdorff, compact, and totally disconnected topological group: that is, a topological group that is also a Stone space.

* Normally-open ( NO ) contacts connect the circuit when the relay is activated ; the circuit is disconnected when the relay is inactive.

Some machines do not support Wake-on-LAN after they have been disconnected from power ( e. g., when power is restored after a power failure ).

The pilot inside the bubble is causally disconnected with its walls and cannot carry out any action outside the bubble.

This perceptive experience is itself the flow of the moving atoms ; and like the changeable and unchangeable forms, the form from which the flow traverses is shed and shattered into even smaller atoms, atoms of which still represent the original form, but they are slightly disconnected and of diverse magnitudes.

The disconnected nature of some of these principles perhaps springs from the fact that the TPS has grown pragmatically since 1948 as it responded to the problems it saw within its own production facilities.

The term " Lake Bonneville drainage " is often used to refer to the assembly of disconnected lakes and rivers ; since the draining happened relatively recently, most of the fish have not had time to evolve into distinct species.

With the inputs disconnected, the gates may be biased into a mode where the outputs are partially conducting ; this leaves the output buffer drawing a great deal of current since it is not fully on or off, creating a low resistance current path between the power supply rails.

* Totally disconnected spaces are T < sub > 1 </ sub > spaces, since points are closed.

The large wages and luxurious lifestyle of trade union leaders undermines their ability to represent their members interests, since they are disconnected from the living and working conditions of large parts of the union movement.

He also presents marriage, in contemporary society, as a key support for children's rights, since — in his view — gay marriages and gay couple adoption rights will lead to a disintegration of the natural link between parenthood and childhood, to the detriment of children who will be disconnected from their roots.

However since churches like the Mulu Wongel church ( started by Ethiopian student movement in the mid-20th century ), remain disconnected from foreign missionaries, their ability to provide equivalent development aid have been reduced.

Concretely, a connected compact 1-manifold with boundary is an interval or a circle ( compactness rules out the open interval and the half-open interval neither of which yields non-trivial embeddings since the open end means that they can be shrunk to a point ), so a possibly disconnected compact 1-manifold is a collection of n intervals and m circles The condition that the boundary of X lies in

Unfortunately he used his wheels against the guards to aid his escape ( since his weapons were disconnected ), causing the release of his lieutenant Fitor ( also a former Guardian ).

In attempts to save the show, the executives decide to introduce Squiggy from Laverne & Shirley into the household, since he is the biggest 1970s television star whose phone has not been disconnected.

" displays " the series ’ nefarious habit of using the first third of the episode as a clearinghouse for disconnected jokes before actually beginning the plot, a blight made that much more glaring here since the only connection to Christmas comes early with the rest not even taking place in winter.

: A closed irreducible orientable 3-manifold M has a submanifold Σ that is a Seifert manifold ( possibly disconnected and with boundary ) whose complement is atoroidal ( and possibly disconnected ).

For a connected manifold, " open " is equivalent to " without boundary and non-compact ", but for a disconnected manifold, open is stronger.

These have two terminals which can be connected or disconnected.

Curl applets can also be written so that they will run off-line when disconnected from the network ( occasionally connected computing ).

It is also path-connected, and is therefore connected as well, though it can be disconnected by removing any one point.

The genus of a connected, orientable surface is an integer representing the maximum number of cuttings along non-intersecting closed simple curves without rendering the resultant manifold disconnected.

With mechanical odometers, the speedometer can be removed from the car dash board and the digits wound back, or the drive cable can be disconnected and connected to another odometer / speedometer pair while on the road.

When a mathematical object has such a property, we say it is connected ; otherwise it is disconnected.

When a disconnected object can be split naturally into connected pieces, each piece is usually called a component ( or connected component ).

It is reproduced in his book The Mind Benders and states, " Anyone connected to him is not to be processed or trained until he or she has disconnected from him in writing.

Individual capacitors are connected or disconnected with switches based on the input.

Indeed, the new spatial form of the mega-city or megalopolis, is defined by Castells as having the contradictory quality of being " globally connected and locally disconnected, physically and socially ".

As a totally disconnected group / has an open compact subgroup, and the pullback of such an open compact subgroup is an open, almost connected subgroup of.

A free long distance telephone call ( such as the information operator from another area code ) was made using a regular telephone, and when the line was connected, a 2600 Hz tone from the blue box was fed into the mouthpiece of the telephone, causing the operator to be disconnected and a free long distance line to be available to the blue box user.

If the two supplies are not synchronised, the short isolating section is disconnected from the supplies, leaving it electrically dead, ensuring that the two grids cannot be connected to each other.

If the normal load cannot be guaranteed to perform this function, perhaps because it can be disconnected, the circuit should include a bleeder resistor connected as close as practical across the capacitor.

They are also totally disconnected ( connected components are points ), scattered ( every non-empty set has an isolated point ; in this case, just take the smallest element ), zero-dimensional ( the topology has a clopen basis: here, write an open interval ( β, γ ) as the union of the clopen intervals ( β, γ '+ 1 )=< nowiki ></ nowiki > for γ '< γ ).