Minimum Linear Arrangement of Generalized Sierpinski Graphs

Abstract

The creation of scientific supercomputers is one of the most pressing issues confronting technology today. Experts in computer science anticipate that future supercomputers will be built on large-scale parallel processing. A system with multiple processors and memories will be used in such a computer. The interconnection network that allows communication between the system’s processors and memories is a critical component of such systems. In the topic of interconnection networks for parallel computer architectures, graph embedding problems have grown in relevance. Network embedding has been recognized as a valuable method for developing efficient algorithms and simulating various architectures in parallel and distributed computing. In this paper, we obtain the maximum subgraph of the generalized Sierpinski graphs $S(n, m), n\geq 2, m\geq 3$, and calculate the minimum linear arrangement of generalized Sierpinski graphs by graph embeddings.