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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 >.
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connected and graph
An ( N, M, D, K, e )- disperser is a bipartite graph with N vertices on the left side, each with degree D, and M vertices on the right side, such that every subset of K vertices on the left side is connected to more than ( 1 − e ) M vertices on the right.
A disconnected graph is not an expander, since the boundary of a connected component is empty.
Every connected graph is an expander ; however, different connected graphs have different expansion parameters.
If the graph G is connected, then the rank of the free group is equal to 1 − χ ( G ): one minus the Euler characteristic of G.
The connected component containing the special vertex contains the objects that can't be collected, while other connected components of the graph only contain garbage.
Often, the model is a complete graph ( i. e. each pair of vertices is connected by an edge ).
* Connected component ( graph theory ), a maximal connected subgraph
Given a connected, undirected graph, a spanning tree of that graph is a subgraph that is a tree and connects all the vertices together.
More generally, any undirected graph ( not necessarily connected ) has a minimum spanning forest, which is a union of minimum spanning trees for its connected components.
If it is constrained to bury the cable only along certain paths, then there would be a graph representing which points are connected by those paths.
For example, if the vertices of the graph represent cities and edge path costs represent driving distances between pairs of cities connected by a direct road, Dijkstra's algorithm can be used to find the shortest route between one city and all other cities.
In mathematics, more specifically graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one simple path.
In other words, any connected graph without cycles is a tree.
* G is connected and the 3-vertex complete graph is not a minor of G.
A forest is an undirected graph, all of whose connected components are trees ; in other words, the graph consists of a disjoint union of trees.
* Every connected graph G admits a spanning tree, which is a tree that contains every vertex of G and whose edges are edges of G.
* Every connected graph with only countably many vertices admits a normal spanning tree.
Kruskal's algorithm is a greedy algorithm in graph theory that finds a minimum spanning tree for a connected weighted graph.
connected and G
Rather the form of the argument is generalized to considering configurations, which are connected subgraphs of G with the degree of each vertex ( in G ) specified.
: G < sub > con </ sub > for the connected component of the identity
: G < sub > sol </ sub > for the largest connected normal solvable subgroup
: G < sub > nil </ sub > for the largest connected normal nilpotent subgroup
: G < sub > con </ sub >/ G < sub > sol </ sub > is a central extension of a product of simple connected Lie groups.
If we require that the Lie group be simply connected, then the global structure is determined by its Lie algebra: for every finite dimensional Lie algebra over F there is a simply connected Lie group G with as Lie algebra, unique up to isomorphism.
Because R is the Lie algebra of the simply connected Lie group R, this induces a Lie group homomorphism c: R → G so that
Although the MOSFET is a four-terminal device with source ( S ), gate ( G ), drain ( D ), and body ( B ) terminals, the body ( or substrate ) of the MOSFET often is connected to the source terminal, making it a three-terminal device like other field-effect transistors.
* G is connected and has no cycles.
* G is connected, but is not connected if any single edge is removed from G.
* Any two vertices in G can be connected by a unique simple path.
* G is connected and has n − 1 edges.
connected and with
All can be connected with the gold circuit from their homes.
Thus, paradoxically, the beat writers resort to `` religious '' metaphors: they are in search of mana, the spiritual, the numinous, but not anything connected with formal religion.
His religiousness is intimately, or dialectically, connected with his sinfulness ; ;
A smart, shrewd and ambitious young man, well connected, and with a knack for getting in the good graces of important people, he was bound to go far.
Trevelyan contributed considerable new knowledge of the issues connected with his subject.
I must, in fairness, take issue with his premise, primarily because the so-called scandals in labor unions were very much connected with business scandals.
On the east side of the island of Manhattan the indifferent hawk knew the East River that connected New York Bay with Long Island Sound.
The Y.M.C.A. and Y.W.C.A. at Carleton are connected with the corresponding national organizations and carry out their general purposes.
Research and development expenditures connected with the reconnaissance satellite SAMOS and the future development of ballistic missile defense systems such as Nike-Zeus are expected to increase substantially.
The first bridge known to have been covered wholly or in part, -- and perhaps the most interesting one, connected Newbury ( now Newburyport ) with Salisbury Point.
Only the independent art schools, that is, those not connected with any university or college, receive severe and separate investigation before accreditation by the various regional organizations.
But Mother insisted, for it is seldom indeed that anyone remotely connected with the cinema is ever received in their exclusive midsts.
The arc voltage was measured with a voltmeter whose terminals were connected to the anode and cathode holders.
Indeed, the spiral Af, with the two endpoints connected by a straight line possesses only one inscribed square.
This exception may be connected with Hoijer's use of a much higher percentage of verbs: 22% of his total list as against 3.5% in mine.
First intercourse for the bride brings with it the various problems connected with virginity and the hymen.
For three years he was connected with the U.S. Naval Observatory and with the U.S. Signal Corps ; ;
Blanche knew something must be causing Stanley's new, strange behavior but she never once connected it with Kitti Walker.
It is connected by teletype with the State Library in Albany, which will supply any book to a system that the system itself cannot provide.
So the plot creaks, the sets are decaying, the costumes are pre-historic, the orchestra was sloppy and not very well connected with what the singers were doing.
But he would fight for his own liberty rather than for any abstract principle connected with it -- such as `` cause ''.
In countries of the British Commonwealth, social anthropology has often been institutionally separate from physical anthropology and primatology, which may be connected with departments of biology or zoology ; and from archaeology, which may be connected with departments of Classics, Egyptology, and the like.
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