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 forest, and every cactus graph is outerplanar.

Every maximal outerplanar graph with n vertices has exactly 2n − 3 edges, and every bounded face of a maximal outerplanar graph is a triangle.

** 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 unital ring other than the trivial ring contains a maximal ideal.

: Every non-empty set A contains an element B which is disjoint from A.

Every computer contains an internal clock that regulates the rate at which instructions are executed and synchronizes all the various computer components.

Cantor points out that his constructions prove more — namely, they provide a new proof of Liouville's theorem: Every interval contains infinitely many transcendental numbers.

Every organic compound contains at least one atom of carbon.

Every ordered field contains an ordered subfield that is isomorphic to the rational numbers.

The revised edition of Robyn was released in the UK in April 2007, and contains two new tracks —" With Every Heartbeat " ( a collaboration with Kleerup ) and " Cobrastyle " ( a cover of a 2006 single by Swedish rockers Teddybears )— alongside slightly altered versions of two of the original songs.

# Every simple path from a given node to any of its descendant leaves contains the same number of black nodes.

Every altar in every Orthodox church contains relics, usually of martyrs.

Every synset contains a group of synonymous words or collocations ( a collocation is a sequence of words that go together to form a specific meaning, such as " car pool "); different senses of a word are in different synsets.

Every PostScript printer contains a RIP in its firmware.

Every one has higher glucose levels for one or two hours after eating food which contains some types of carbohydrates.

Every bag of blood ( 450 – 500 ml ) contains 200 – 250 milligrams of iron.

Every temple of The Church of Jesus Christ of Latter-day Saints ( LDS Church ) contains a baptismal font on twelve oxen that is modeled after the molten sea.

Every issue of GAMES Magazine contains a large crossword with a double clue list, under the title The World's Most Ornery Crossword ; both lists are straight and arrive at the same solution, but one list is significantly more challenging than the other.

Every gap sequence that contains 1 yields a correct sort ; however, the properties of thus obtained versions of Shellsort may be very different.

Every prostaglandin contains 20 carbon atoms, including a 5-carbon ring.

Every device contains at least one swap chain.

Every living organism contains DNA, RNA, and proteins.

Every game in the Mario Party series contains 50 to 80 mini-games of a few different types.

The offset part of the logical address contains an offset inside the segment, i. e. the physical address can be calculated as ( if the address line A20 is enabled ), respectively ( segment_part × 16 + offset ) mod 2 < sup > 20 </ sup > ( if A20 is off ) Every segment has a size of 2 < sup > 16 </ sup > bytes.

Every chapter contains a comprehensive compilation all of the published examples of the reaction organized in tables according to the structure of the starting material.

Every Riemann surface is a two-dimensional real analytic manifold ( i. e., a surface ), but it contains more structure ( specifically a complex structure ) which is needed for the unambiguous definition of holomorphic functions.