The Graph of e-Abacus Diagram

Abstract

Since 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 process

Adding Rows in Main e-Abacus Diagrams

“…and we mean here that we delete all the rows that come at the beginning of the bead(s) from without any space between them within the same row but without using the e-abacus diagram? The answer was yes, through what was presented by Satyanarayana and Prasad [6], Rosen [7] Hashim [8], as follows:…”

On Graph- Syriac Letters Partition

“…To make a special directed graph for the e-Abacus Diagram for Syriac letters, we will benefit from the idea that was found by [3], which is at the beginning of the representation of each number of beta numbers represented by (▪) expressed by 1and (-) expressed by 0 and thus The Abacus diagram will be transformed into a matrix whose elements are zero and one, as it is shown in Figure 2:…”

“…1 2 3 4 5 6 7 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 3 0 0 1 0 0 0 0 4 0 0 0 1 0 1 1 5 0 0 0 0 1 0 1 6 1 1 1 1 1 1 1 7 0 0 0 0 0 0 0 code ‫)ܡ(‬ = (0,0,1,3,2,7,0; 1,1,2,2,2,2,3) But if we want to be a word in the Syriac language by using the graph and the neighborhood matrix, then we know that each letter will consist of 7 rows and 7 columns. As it is done in [ 3], we add rows by 7(𝜃 − 1) all elements are zeros, and thus a square matrix will be formed consisting of a new capacity, which is 7𝜃 * 7𝜃, and the code of a word consisting of f letters is:…”

“…Sami and Mahmoud introduced [1], [2] different types of encoding Syriac letters. Syriac language is an ancient that derived from the Aramaic language, so in this work, we try to employ the method that used by Ahmed and Mahmoud in [3] due to the increasing of the difficulty of cracking the code as we previously found in [1]. In the beginning, we will introduce the important concepts for the work.…”

Inclusion Mapping and Partition Theory

“…Previous research has attempted to make partition theory a focus with a range of fields, including coding, graph theory see [4] and so on, to get the most of it, this time with one of the mappings. Now we'll try to show a connection between inclusion mapping and partition theory by illustrating one of its features.…”