On Some Properties of Pseudo-Semiregular Graphs

The application of the bipartite pseudo-semiregular graphs (BPS graphs) has recently had a growing importance in mathematical chemistry, mainly for QSAR (quantitative structure-activity relations) and QSPR (quantitative structure-property relations) studies. The aim of the research presented herein, is to give a systematic survey on the fundamental characteristics of BPS graphs and summarize some novel results concerning their structural-topological properties. We propose some practical methods for the construction of BPS graphs from various parent graphs. Moreover, a simple procedure is outlined by which a finite set of BPS graphs possessing the same spectral radius or the same second Zagreb index can be generated. Additionally, as a result of our investigations, it is verified that there is a strong correspondence between BPS graphs and balanced tree graphs of diameter 4.