04f4cd6d-0879-4acc-bd28-56307a4e58af20210222121924833wseamdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON MATHEMATICS1109-276910.37394/23206http://wseas.org/wseas/cms.action?id=40512720202720201910.37394/23206.2020.19http://wseas.org/wseas/cms.action?id=23185The Graph of e-Abacus DiagramAhmed MohammedAliDepartment of Mathematics, College of Computer science and Mathematics, University of Mosul, Mosul, IRAQAmmarSeddiq MahmoodDepartment of Mathematics, College of Education for Pure science, University of Mosul, Mosul, IRAQSince James introduced the idea of an e-abacus diagram in 1978, this topic plays important roles with many topics, especially in algebra. In this paper, we will present new insights on this topic so that it appears to us as a graph theory; specifically a directed graph, according to certain conditions, to be a new start with another field. This proposed technique will be applied to the model that was approved by Mahmood and Mahmood in 2019 on English letters and to see how successful we are on Letter-Word-Sentence. It is completely natural that this method will have a new and very difficult method as an entrance to a new type of encryption process1022202010222020486497https://www.wseas.org/multimedia/journals/mathematics/2020/b065106-1312.pdf10.37394/23206.2020.19.52https://www.wseas.org/multimedia/journals/mathematics/2020/b065106-1312.pdfR. Balakrishnan and K. Ranganathan, A Textbook of Graph Theory, Springer Science, New York 2012.G. Chartrand and L. Lesniak, Graphs and Digraphs, 6th ed., Wadsworth and Brooks / Cole. California, 2016.J.C. Fournier, Graph Theory and Applications, Library of Congress Cataloging-in- Publication Data, 2009. W. Fulton, Young Tableaux, with Applications to Representation Theory and Geometry, Cambridge University Press, 1997.G. D. James, Some combinatorial results involving Young diagrams, Mathematical Proceeding of the Cambridge Philosophical Society, Vol.83,1978,pp. 1-10. L. G. Jonathan, Y. Jay and A.Mark, Graph Theory and Its Applications, 3rd edition. LLC CRC Press is an imprint of Taylor & Francis Group, 2019. A. S. Mahmood, Replace the content in e-abacus diagram. Open Access Library J., Vol.7,2020, pp.1-6. A. B. Mahmood and A. S. Mahmood, Secret-word by e-abacus diagram I. Iraqi J. of Science, Vol.60, No.3, 2019, pp.638-646. A. B. Mahmood and A. S. Mahmood, Secret-text by e-abacus diagram II. Iraqi J. of Science, Vol.60, No.4,2019, pp.840-846. 10.1090/ulect/015/02A. Mathas, Iwahori-Hecke Algebras and Schur Algebras of the Symmetric Group, University Lecture Series, Vol.15, 1999. D. Matthias and E. Frank, Quantitative Graph Theory Mathematical Foundations and Applications, Chapman and Hall/CRC. 2019.J. W. Robin, Introduction to Graph Theory, 4th edition, Library of Congress Cataloging in Publication Data, 1996.