Wirelength of embedding complete multipartite graphs into certain graphs

Abstract

Graph embedding is an important technique that maps a guest graph into a host graph, usually an interconnection network. Many applications can be modeled as graph embedding. In architecture simulation, graph embedding has been known as a powerful tool for implementation of parallel algorithms or simulation of different interconnection networks. The quality of an embedding can be measured by certain cost criteria. One of these criteria is the wirelength and has been well studied by many authors (Lai and Tsai, 2010 [18]; Fan and Jia, 2007 [10]; Han et al., 2010 [15]; Fang and Lai, 2005 [11]; Park and Chwa, 2000 [23]; Rajasingh et al., 2004; Yang et al., 2010; Yang, 2009 [27]; Manuel et al., 2009; Bezrukov et al., 1998; Rostami and Habibi, 2008 [26]; Choudum and Nahdini, 2004 [7]; Guu, 1997 [14]). In this paper, we compute the exact wirelength of embedding complete multipartite graphs into certain graphs, such as path, cycle, wheel, hypertree, cylinder, torus and 3-regular circulant graphs.