Speaker
Description
In this paper, I study perfect codes and the biclique partition number in graphs, with a special focus on Cayley sum graphs and signed graphs. Perfect codes, which play an important role in coding theory and error correction, were first introduced in graphs by Norman Biggs. Later, Zhou (2016) extended this concept to Cayley graphs and investigated their structural properties. Building on these works, I further study perfect codes in Cayley sum graphs and introduce perfect codes in Cayley sum signed graphs.
In this paper, I also investigate the biclique partition number of Cayley sum graphs. Determining the biclique partition number of a graph is a fundamental and NP-hard problem in graph theory. This number represents the minimum collection of complete bipartite subgraphs required to cover all edges of a graph. I determine the biclique partition number for a specific class of bi-regular graphs arising from Cayley sum graphs. Moreover, I introduce the notions of positive and negative biclique partitions in signed graphs, which have potential applications in recommender systems.