Vector weighted Stirling numbers and an application in graph theory

Fahimeh Esmaeeli, Ahmad Erfanian, Madjid Mirzavaziri
2021 Electronic Journal of Graph Theory and Applications  
We introduce \textit{vector weighted Stirling numbers}, which are a generalization of ordinary Stirling numbers and restricted Stirling numbers. Some relations between vector weighted Stirling numbers and ordinary Stirling numbers and some of their applications are stated. Moreover, as an application of vector weighted Stirling numbers of the second kind in graph theory, we compute the number of maximal independent sets of different sizes in k-intersection graphs.
doi:10.5614/ejgta.2021.9.1.20 doaj:2dc0d446e65a4e5e82cef39c6c9d3acf fatcat:sko3mpstijeddd2os3jhlj2e4m