Embedding complete multi-partite graphs into Cartesian product of paths and cycles

R. Sundara Rajan (Department of Mathematics, Hindustan Institute of Technology and Science, Chennai, 603 103.)
A. Arul Shantrinal (Department of Mathematics, Hindustan Institute of Technology and Science, Chennai, 603 103.)
T.M. Rajalaxmi (Department of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, Chennai, 603 110.)
Jianxi Fan (School of Computer Science and Technology, Soochow University, Suzhou 215006, China)
Weibei Fan (School of Computer Science & Technology, Nanjing University of Posts and Telecommunications, Jiangsu 210049, China)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 9, No 2 (2021): Electronic Journal of Graph Theory and Applications

Graph embedding is a powerful method in parallel computing that maps a guest network G into a host network H. The performance of an embedding can be evaluated by certain parameters, such as the dilation, the edge congestion, and the wirelength. In this manuscript, we obtain the wirelength (exact and minimum) of embedding complete multi-partite graphs into Cartesian product of paths and/or cycles, which include n-cube, n-dimensional mesh (grid), n-dimensional cylinder, and n-dimensional torus, etc., as the subfamilies.