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Page "Outerplanar graph" ¶ 12
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Every and forest
During his career as writer and while living in the mountains, Muir continued to experience the " presence of the divine in nature ," writes Holmes From Travels in Alaska: " Every particle of rock or water or air has God by its side leading it the way it should go ; The clearest way into the Universe is through a forest wilderness ; In God's wildness is the hope of the world.
She also performed a song for the flash anime of Xenosaga-A Missing Year and the anime series El Cazador de la Bruja ( performing forest and I reach for the sun ) and Kajiura's latest Pandora Hearts ( performing Every time you Kissed Me which is now featured on the second original soundtrack published by JVC Music in Japan.
Every autumn, the dried needles of this tree forms a dense carpet on the forest floor, which the locals gather in large bundles to serve as bedding for their cattle, for the year round.
Every year October month the village people go to the forest.

Every and every
Every path from back door to barn was covered by a grape-arbor, and every yard had its fruit trees.
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 pitch in the game brought forth a howl from the enraptured audience and every fly ball the visitors dropped ( and because their right fielder was still a little fuzzy from drink, they dropped many ) called forth yelps of derision.
Every man in every one of these houses is a Night Rider.
** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.
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 quadratic Bézier curve is also a cubic Bézier curve, and more generally, every degree n Bézier curve is also a degree m curve for any m > n. In detail, a degree n curve with control points P < sub > 0 </ sub >, …, P < sub > n </ sub > is equivalent ( including the parametrization ) to the degree n + 1 curve with control points P '< sub > 0 </ sub >, …, P '< sub > n + 1 </ sub >, where.
* Every unital real Banach algebra with no zero divisors, and in which every principal ideal is closed, is isomorphic to the reals, the complexes, or the quaternions.
Every cleric in Holy Orders and every member of a religious order must publicly join in or privately read aloud ( i. e. using the lips as well as the eyes — it takes about two hours in this way ) the whole of the Breviary services allotted for each day.
Every retraction is an epimorphism, and every section is a monomorphism.
Every regular language is context-free, every context-free language, not containing the empty string, is context-sensitive and every context-sensitive language is recursive and every recursive language is recursively enumerable.
Every grammar in Chomsky normal form is context-free, and conversely, every context-free grammar can be transformed into an equivalent one which is in Chomsky normal form.
Every corporation, whether financial or union, as well as every division of the administration, were set up as branches of the party, the CEOs, Union leaders, and division directors being sworn-in as section presidents of the party.
Every gun that is made, every warship launched, every rocket fired signifies, in the final sense, a theft from those who hunger and are not fed, those who are cold and are not clothed.
Every mental phenomenon, every psychological act, has a content, is directed at an object ( the intentional object ).
Every step had been carefully planned, every calculation meticulously done.
" More immediately, though, he called for a massive build-up of U. S. arms production: " Every realist knows that the democratic way of life is at this moment being ' directly assailed in every part of the world … The need of the moment is that our actions and our policy should be devoted primarily — almost exclusively — to meeting this foreign peril.
Every continuous map f: X → Y induces an algebra homomorphism C ( f ): C ( Y ) → C ( X ) by the rule C ( f )( φ ) = φ o f for every φ in C ( Y ).
Every galaxy of sufficient mass in the Local Group has an associated group of globular clusters, and almost every large galaxy surveyed has been found to possess a system of globular clusters.
Every valley, every cliff, to my look is beautiful.
Every seminorm on V ( in particular, every norm on V ) is sublinear.
Every little change in every little property would mean the whole thing is destroyed.

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 tree is a bipartite graph and a median graph.
Every tree with only countably many vertices is a planar graph.
* 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.
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 planar graph whose faces all have even length is bipartite.
Every vertex of this graph has an even degree, therefore this is an Eulerian graph.
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 outerplanar graph is a planar graph.
Every outerplanar graph is also a subgraph of a series-parallel graph.
Every maximal outerplanar graph with n vertices has exactly 2n − 3 edges, and every bounded face of a maximal outerplanar graph is a triangle.

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