[permalink] [id link]

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.

from
Wikipedia

## Some Related Sentences

Every and graph

__Every__

**connected**

__graph__

**is**

**an**expander ; however

**,**different

**connected**graphs

**have**different expansion parameters

**.**

:"[...]

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

__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**.**
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__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__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

**.**

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__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__broadcasting company

**has**members

**and**

**the**number

**of**members gives

**them**

**a**status

**that**

**is**

__connected__to

**the**number

**of**hours

**of**broadcasting

**.**

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

**.**

0.296 seconds.