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Equivalence relation (X) Geometry (X)

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 Book Id: WPLBN0002097092 ► Abstract Full Text Search Details...s-manifolds are a very restricted subclass of the 7 polyhedral surfaces. The relationship between polyhedral surfaces and Riemannian manifolds is... ... The non-Euclidean vertices introduce a sort of curvature, and this affects the relationships between s-lines. The topology of an s-manifold can all... ...lines being parallel or not parallel at different points along them, since this relationship between s-lines changes as 21 we move from point to ... ...y, to change from region to region, this does not necessarily carry over to the relationships between lines, or 26 geodesics. This is, in fact, o... ...e to S-deny all of Hilbert’s axioms, and our choice to have congruence to be an equivalence relation further reduces our ability to S-deny Hilbert’s... ...all of Hilbert’s axioms, and our choice to have congruence to be an equivalence relation further reduces our ability to S-deny Hilbert’s axioms. Mos... ...nsitive. In fact, our definition of s- congruence satisfies the properties of an equivalence relation, i.e., it is reflexive, symmetric, and transiti... ...lexive, symmetric, and transitive. Using a notion of congruence that was not an equivalence relation would complicate the study of all related issue...
 Date: 2013, Volume 3, October 2010 Book Id: WPLBN0002828350 ► Abstract Description Details... Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitational fields; Mathemati... Excerpt Details... how the Zagreb indices, a particular case of Smarandache-Zagreb index of a graph changes with these operators and extended these results to obtain a relation connecting the Zagreb index on operators. Key Words: Subdivision graph, ladder graph, Smarandache-Zagreb index, Zagreb index, graph operators. ... Table of Contents Details...SI Hypergraph Partitioning Using Taguchi Methods BY P.SUBBARAJ, S.SARAVANASANKAR and S.ANAND . . . . . . . . . . . . . . . . 69 Negation Switching Equivalence in Signed Graphs BY P.SIVA KOTA REDDY, K.SHIVASHANKARA and K.V.MADHUSUDHAN. . . . . . 85 Weak and Strong Reinforcement Number For a Graph BY PINAR DUNDAR, TUFAN TURACI and DERYA DOGAN. . . . . . . . . . . . . ....
 Date: 2013, Volume 4, December 2010 Book Id: WPLBN0002828354 ► Abstract Description Details... Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitational fields; Mathemati... Table of Contents Details.... . . . . . . . 70 Entire Semitotal-Point Domination in Graphs BY B.BASAVANAGOUD, S.M.HOSAMANI and S.H.MALGHAN. . . . . . . . . . . . . . .79 On k-Equivalence Domination in Graphs BY S.ARUMUGAM and M.SUNDARAKANNAN. . . . . . . . . . . . . . . . . . . . . . . 86 On Near Mean Graphs BY A.NAGARAJAN, A.NELLAI MURUGAN and S.NAVANEETHA KRISHNAN. . . . . . 94 On Pathos Lic...
 Book Id: WPLBN0002097095 ► Abstract Full Text Search Details... manifolds with higher dimension are inspired by the Riemann surfaces. The relation of maps with Riemann surfaces has been known in 80s in the last ce... ...etries, maps and the semi-arc automorphism group of a graph. Preface ii A relation for maps and Smarandache manifolds (abbreviated s-manifolds) and a... ...oted maps are established in this chapter. The last section determines the relation of the number of embeddings and rooted maps of a graph on genus. A... ...me for enumerating maps underlying a graph.........................17 §4 A relation among the total embeddings and rooted maps of a graph on genus20 4... ...pty boundary and to be analytic functions. Whence, we have the following relation: {Riemann Sufaces}⊂{Klein surfaces}. The upper half planeH ={z∈C|I... ...re exists an isomorphism ζ between them induced by an element ξ. Call ζ an equivalence between M 1 ,M 2 . Certainly, on an orientable surface, an equi... ...t1 2 Γ such that P ζ 1 = P 2 or P ζ 1 = P −1 2 . Proof By the deﬁnition of equivalence between maps, if κ is an equivalence between M 1 and M 2 , then... ...ducedtheconformalmappingbetween maps. Then, how can we deﬁne the conformal equivalence for maps enabling us to get the uniformiza- tion theorem of map...
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