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...ACES AND SMARANDACHE GEOMETRIES American Research Press Rehoboth, NM 2005 Linfan MAO Institute of Systems Science Academy of Mathematics and Systems ... ...D SMARANDACHE GEOMETRIES American Research Press Rehoboth, NM 2005 Linfan MAO Institute of Systems Science Academy of Mathematics and Systems Chinese... ...ty, Mansfield, PA 16933, USA. Copyright 2005 by American Research Press and Linfan Mao Rehoboth, Box 141 NM 87322, USA Many books can be downloaded fro... ...sfield, PA 16933, USA. Copyright 2005 by American Research Press and Linfan Mao Rehoboth, Box 141 NM 87322, USA Many books can be downloaded from the f... ...l presented here. Any suggestions for improving this book are welcome. L.F.Mao AMSS, Beijing June, 2005 Contents Preface................................ ...ometry of Curves and Surfaces, Pearson Education asia Ltd (2004). [43] L.F.Mao, A census of maps on surface with given underlying graph, A doctor thes... ..., A doctor thesis in Northern Jiaotong University, Beijing, 2002. [44] L.F.Mao and Y.P.Liu, New automorphism groups identity of trees, Chinese Advance... ...ormization theorem 104 voltage map 33 walk 5 y-linear 24 About the Author LinfanMaoisapost-doctorintheAcademyofMathematicsandSystemsofChinese Academy...

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...Combinatorial Speculation and Combinatorial Conjecture for Mathematics BY LINFAN MAO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Structures of Cycle Bases with Some Extremal Properties BY HAN REN and YUN BAI . . . ...

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...Contents Extending Homomorphism Theorem to Multi-Systems BY LINFAN MAO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 01 A Double Cryptography Using the Smarandache Keedwell Cross Inverse Quasigroup BY T. G. JA´IY´EOL´A . . . . . . . . . . . . . . . . . . . . . . ...

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... . . . . . . . . . . . . . . . . . . . . . . . . . .06 Curvature Equations on Combinatorial Manifolds with Applications to Theoretical Physics BY LINFAN MAO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16 A Pair of Smarandachely Isotopic Quasigroups and Loops of the Same Variety BY T. G. JA´IY´EOL´A . . . . . . . . . . . . . . . . . . . . . ....

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...ns with Disability (PWD) Using FRMs BY W.B.VASANTHA KANDASAMY, A.PRAVEEN PRAKASH AND K.THIRUSANGU 01 Topological Multi-groups and Multi-fields BY LINFAN MAO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 08 Shortest Co-cycle Bases of Graphs BY HAN REN AND JING HAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 On Involute a...

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...Sequences on Graphs with Symmetries Linfan Mao Chinese Academy of Mathematics and System Science, Beijing, 10080, P.R.China Beijing Institute of Civil Engineering and Architecture, Beijing, 100044, P.R.China E-mail: maolinfan@163.com Abstract: An interestin...

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... Lucas Graceful Labeling for Some Graphs BY M.A.PERUMAL, S.NAVANEETHAKRISHNAN AND A.NAGARAJAN . . . . . 01 Sequences on Graphs with Symmetries BY LINFAN MAO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Supermagic Coverings of Some Simple Graphs BY P.JEYANTHI AND P.SELVAGOPAL . . . . . . . . . . . . . . . . . . . . . . . 33 Elementary Abelia...

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... S.PANAYAPPAN and VERNOLD VIVIN.J . . . . . . . . . . . . 98 Labeling, Covering and Decomposing of Graphs – Smarandache’s Notion in Graph Theory BY LINFAN MAO . . . . . . . . . . . . . . . . . . . . . . . . . . . 108...

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... Minkowski Space-time BY MELIH TURGUT AND SUHA YILMAZ . . . . . . . . . . . . . . . . . . . . . . . 17 Combinatorially Riemannian Submanifolds BY LINFAN MAO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Smarandache Half-Groups BY ARUN S.MUKTIBODH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46 On Smarandache Bryant Schnei...

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...Contents Combinatorial Fields - An Introduction BY LINFAN MAO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .01 A Spacetime Geodesics of the Schwarzschild Space and Its Deformation Retract BY H. RAFAT. . . . . . . . . . . . . . . . . . . . . . . . . . ....