Partially balanced network designs and graph codes generation

Abstract

<abstract> <p>Partial balanced incomplete block designs have a wide range of applications in many areas. Such designs provide advantages over fully balanced incomplete block designs as they allow for designs with a low number of blocks and different associations. This paper introduces a class of partially balanced incomplete designs. We call it partially balanced network designs (PBNDs). The fundamentals and properties of PBNDs are studied. We are concerned with modeling PBNDs as graph designs. Some direct constructions of small PBNDs and generalized PBNDs are introduced. Besides that, we show that our modeling yields an effective utilization of PNBDs in constructing graph codes. Here, we are interested in constructing graph codes from bipartite graphs. We have proved that these codes have good characteristics for error detection and correction. In the end, the paper introduces a novel technique for generating new codes from already constructed codes. This technique results in increasing the ability to correct errors.</p> </abstract>

Decompositions of Circulant-Balanced Complete Multipartite Graphs Based on a Novel Labelling Approach

“…Graph theory is extremely important in complex systems, particularly in computer science. Many scientific areas use graph theory, including engineering, coding [4,5], operational research, biological sciences, and management sciences. For applied scientists and engineers, graph theory is a strong and vital science for evaluating and inventing solutions for a variety of issues.…”