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Every connected graph is an expander ; however, different connected graphs have different expansion parameters.

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## Some Related Sentences

Every and connected

__Every__individual

**is**

__connected__with the rest of the world

**,**and the universe

**is**fashioned for universal harmony

**.**

__Every__aspect of life

**,**every word

**,**plant

**,**animal and ritual was

__connected__to the power and authority of the gods

**.**

*

__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__aspect of life

**,**every word

**,**plant

**,**animal and ritual was

__connected__to the power and authority of the gods

**.**

The generalized Poincaré conjecture states that

__Every__simply__connected__**,**closed n-manifold**is**homeomorphic to the n-sphere**.**__Every__closed 3-manifold has a prime decomposition: this means it

**is**the

__connected__sum of prime three-manifolds ( this decomposition

**is**essentially unique except for a small problem in the case of non-orientable manifolds ).

__Every__part of it

**,**including the blue and white colors ( see below ), the cross

**,**as well as the stripe arrangement can be

__connected__to very old historical elements

**;**

**however**it

**is**difficult to establish " continuity ", especially as there

**is**no record of the exact reasoning behind its official adoption in early 1822

**.**

__Every__Eulerian orientation of a

__connected__

**graph**

**is**a strong orientation

**,**

**an**orientation that makes the resulting directed

**graph**strongly

__connected__

**.**

__Every__maximal outerplanar

**graph**satisfies a stronger condition than Hamiltonicity: it

**is**node pancyclic

**,**meaning that for every vertex v and every k in the range from three to the number of vertices in the

**graph**

**,**there

**is**a length-k cycle containing v

**.**A cycle of this length may be found by repeatedly removing a triangle that

**is**

__connected__to the rest of the

**graph**by a single edge

**,**such that the removed vertex

**is**not v

**,**until the outer face of the remaining

**graph**has length k

**.**

__Every__broadcasting company has members and the number of members gives them a status that

**is**

__connected__to the number of hours of broadcasting

**.**

__Every__

**graph**( that

**is**

__connected__and not a tree ) has multiple spanning trees

**,**so we once again

**have**

**an**example where the problem itself allows multiple possible outcomes

**,**and the algorithm chosen can arrive at any one of them

**,**but will never arrive at something else

**.**

This flat may be identified with the partition of the vertices of into the

__connected__components of the subgraph formed by:__Every__set of edges having the same closure as gives rise to the same partition of the vertices**,**and may be recovered from the partition of the vertices**,**as it consists of the edges whose endpoints both belong to the same set in the partition**.**__Every__rational variety

**,**including the projective spaces

**,**

**is**rationally

__connected__

**,**but the converse

**is**false

**.**

*

__Every__external device__connected__to the Freebox player**is**available to that device only but the devices__connected__to the Freebox Server are available to every Freebox player__connected__**.**__Every__extra foot of cord increases the electrical resistance

**,**which decreases the power the cord can deliver to

__connected__devices

**.**

__Every__closed

**,**orientable

**,**

__connected__3-manifold

**is**obtained by performing Dehn surgery on a link in the 3-sphere

**.**

__Every__

__connected__symmetric

**graph**must thus be both vertex-transitive and edge-transitive

**,**and the converse

**is**true for

**graphs**of odd degree

**.**

Every and graph

:"[...]

__Every__invariant and co-variant thus becomes expressible by a__graph__precisely identical with a Kekuléan diagram or chemicograph**.**
In mathematics

**,**Tait's conjecture states that "__Every__3-connected planar cubic__graph__has a Hamiltonian cycle ( along the edges ) through all its vertices ".__Every__homomorphism of the Petersen

__graph__to itself that doesn't identify adjacent vertices

**is**

**an**automorphism

**.**

__Every__directed acyclic

__graph__has a topological ordering

**,**

**an**ordering of the vertices such that the starting endpoint of every edge occurs earlier in the ordering than the ending endpoint of the edge

**.**

__Every__maximal outerplanar

__graph__with n vertices has exactly 2n − 3 edges

**,**and every bounded face of a maximal outerplanar

__graph__

**is**a triangle

**.**

Every and is

__Every__legislator from Brasstown Bald to Folkston

__is__going to

**have**his every vote subjected to the closest scrutiny as a test of his political allegiances

**,**not his convictions

**.**

__Every__detail in his interpretation has been beautifully thought out

**,**and of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation (

**an**obvious indication that he

__is__playing with Viennese musicians )

**,**and the gossamer shading throughout

**.**

__Every__taxpayer

__is__well aware of the vast size of our annual defense budget and most of our readers also realize that a large portion of these expenditures go for military electronics

**.**

__Every__few days

**,**in the early morning

**,**as the work progressed

**,**twenty men would appear to push it ahead and to shift the plank foundation that distributed its weight widely on the Rotunda pavement

**,**supported as it

__is__by ancient brick vaulting

**.**

__Every__dream

**,**and this

__is__true of a mental image of any type even though it may be readily interpreted into its equivalent of wakeful thought

**,**

__is__a psychic phenomenon for which no explanation

__is__available

**.**

__Every__library borrower

**,**or at least those whose taste goes beyond the five-cent fiction rentals

**,**knows what it

__is__to hear the librarian say apologetically

**,**`` I'm sorry

**,**but we don't

**have**that book

**.**

__Every__community

**,**if it

__is__alive has a spirit

**,**and that spirit

__is__the center of its unity and identity

**.**

The restricted principle "

__Every__partially ordered set has a maximal totally ordered subset "__is__also equivalent to AC over ZF**.**__Every__natural-born citizen of a foreign state who

__is__also

**an**American citizen and every natural-born American citizen who

__is__a citizen of a foreign land owes a double allegiance

**,**one to the United States

**,**and one to his homeland ( in the event of

**an**immigrant becoming a citizen of the US ), or to his adopted land ( in the event of

**an**emigrant natural born citizen of the US becoming a citizen of another nation ).

__Every__line of written text

__is__a mere reflection of references from any of a multitude of traditions

**,**or

**,**as Barthes puts it

**,**" the text

__is__a tissue of quotations drawn from the innumerable centres of culture "; it

__is__never original

**.**

__Every__year

**,**on the last Sunday in April

**,**there

__is__

**an**ice fishing competition in the frozen estuarine waters of the Anadyr River's mouth

**.**

__Every__lattice element of the structure

__is__in its proper place

**,**whether it

__is__a single atom or a molecular grouping

**.**

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