Similarly, a graph is 2-connected if we must remove at least two vertices from it, to create a disconnected graph.

* Similarly, if is the finite cyclic group of order n and the set S consists of two elements, the standard generator of G and its inverse, then the Cayley graph is the cycle.

Similarly, an edge coloring assigns a color to each edge so that no two adjacent edges share the same color, and a face coloring of a planar graph assigns a color to each face or region so that no two faces that share a boundary have the same color.

Similarly, if Peggy knew in advance that Victor would ask to see the isomorphism then she could simply generate an isomorphic graph H ( in which she also does not know a Hamiltonian Cycle ).

Similarly, if, then the graph of gives the lower half of the circle.

Similarly, the complement of an odd cycle of length 2k + 1 cannot be perfect, because its chromatic number is k + 1 and its clique number is k. ( Alternatively, the imperfection of this graph follows from the perfect graph theorem and the imperfection of the complementary odd cycle ).

Similarly, a subsidy on the commodity does not directly change the demand curve, if the price axis in the graph represents the price after deduction of the subsidy.

Similarly, Robert Nozick argues for a theory that is mostly consequentialist, but incorporates inviolable " side-constraints " which restrict the sort of actions agents are permitted to do.

Similarly, a consequentialist theory may aim at the maximization of a particular virtue or set of virtues.

Similarly, Herman's theory of doublespeak having an inherent nature to be manipulative and Chomsky's theory of ' dichotomization ' relates directly to the practice of doublespeak and how doublespeak is deliberately deceptive in nature.

Similarly, demand-and-supply theory predicts a new price-quantity combination from a shift in demand ( as to the figure ), or in supply.

Similarly, in Thermal quantum field theory a compactification of the euclidean time dimension leads to the Matsubara frequencies and thus to a discretized thermal energy spectrum.

Similarly, a mathematician does not restrict his study of numbers to the integers ; rather he considers more abstract structures such as rings, and in particular number rings in the context of algebraic number theory.

Despite the nomenclature, the " field " under study is the gravitational potential, φ, rather than the gravitational field, g. Similarly, when classical field theory is used to study electromagnetism, the " field " of interest is the electromagnetic four-potential ( V / c, A ), rather than the electric and magnetic fields E and B.

Similarly, Belgium took no direct influence from the Statute or English copyright theory, but Joris Deene of the University of Ghent identifies an indirect influence " at two levels "; the criteria for what constitutes copyrightable material, which comes from the work of English theorists such as Locke and Edward Young, and the underlying justification of copyright law.

Similarly, in the de Broglie – Bohm theory, there are anomalous initial conditions which would produce measurement statistics in violation of the Born rule ( i. e., in conflict with the predictions of standard quantum theory ).

Similarly, deep structure was devised largely for technical reasons relating to early semantic theory.

Similarly, an experiment that provides a counterexample can disprove a theory or hypothesis.

Similarly, liberalism draws upon the work of Kant and Rousseau, with the work of the former often being cited as the first elaboration of democratic peace theory.

Similarly, probability theory states that the probability of an event can be described by a combination of the probabilities of certain specific other events ( see Mathematical treatment ).

4 ) Similarly, the Moore – Smith theory of convergence via nets, as supplemented by Kelley's notion of a universal net, leads to the criterion that a space is compact if and only if each universal net on the space converges.

Similarly, in social theory, a single direct action producing a social change is a first-order control system.

Similarly, many who avail themselves of magic do so without feeling the need to understand a causal theory behind it.

His need to provide a liberal justification for criminal law practice thus lead him to moral philosophy, and to the development of an original " consensual " theory of punishment which combined the merits of the retributive and utilitarian ( see deterrence ) varieties while avoiding their respective difficulties Similarly, the problems presented by the characterization of criminal conduct stimulated his work in the field of philosophy of action.

Similarly, object relations theory would point to the way ' in perversion there is the refusal, the terror of strangeness '; to the way ' the " pervert "... attacks imaginative elaboration through compulsive action with an accomplice ; and this is done to mask psychic pain '.

Similarly, Fermat's last theorem is stated in term of elementary arithmetic, which is a part of commutative algebra, but its proof involves deep results of both algebraic number theory and algebraic geometry.

Similarly, a theory consists of some indeterminate conjunction of hypotheses,

" Similarly, Maria Todorova notes that, although it minimized the Ottoman contribution and displayed " emotional or evaluative overtones ", such a perspective ran against the divisive interpretations of the Balkans, offering a working paradigm for a global history of the region: " Although Iorga's theory may be today 2009 no more than an exotic episode in the development of Balkan historiography, his formulation Byzance après Byzance is alive not only because it was a fortunate phrase but because it reflects more than its creator would intimate.

Similarly, every cobordism theory has an extraordinary cohomology theory, with homology (" bordism ") groups and cohomology (" cobordism ") groups for any space.

Similarly in Illinois there is Lincoln country to be seen -- his tomb and other landmarks.

Similarly, at the opposite end of the market cycle, towards the end of an intermediate or major decline, usually while the bottom is being formed on the price chart, it is characteristic that an increase is noticed in odd-lot selling again alerting the chartist that a bottom is becoming a greater likelihood.

Similarly, the American Cancer Society ( ACS ), the Arthritis and Rheumatism Foundation, and the BBB have each stated lately that medical quackery is at a new high.

Similarly, a girl who graduates with a good working knowledge of stenography and the use of clerical machines and who is able to get a job at once may wish to improve her skill and knowledge by a year or two of further study in a community college or secretarial school.

Similarly, the Italian verb corresponding to ' spell ( out )', compitare, is unknown to many Italians because the act of spelling itself is rarely needed: Italian spelling is highly phonemic.

Similarly, Helen Keller stated that " Life is either a daring adventure or nothing.

Similarly, although a subset of the real numbers that is not Lebesgue measurable can be proven to exist using the axiom of choice, it is consistent that no such set is definable.

Similarly, all the statements listed below which require choice or some weaker version thereof for their proof are unprovable in ZF, but since each is provable in ZF plus the axiom of choice, there are models of ZF in which each statement is true.

Similarly in St Peter: " Christ .. Who verily was foreordained before the foundation of the world, but was manifest in these last times for you " ( 1 Peter 1: 20 ), and " But the end of all things is at hand " ( 1 Peter 4: 7 ).

Similarly, the subset order ⊆ on the subsets of any given set is antisymmetric: given two sets A and B, if every element in A also is in B and every element in B is also in A, then A and B must contain all the same elements and therefore be equal:

Similarly, in the Greek Magical Papyri, the term " Aion " is often used to denote the All, or the supreme aspect of God

Similarly, " suprarenal " is derived from supra-( Latin, " above ") and renes.

Similarly the freehold of a benefice, on the death of the incumbent, is said to be in abeyance until the next incumbent takes possession.

Similarly, the use of excessively high doses ( often the result of polypharmacy ) continues despite clinical guidelines and evidence indicating that it is usually no more effective but is usually more harmful.