Vector weighted Stirling numbers and an application in graph theory

Fahimeh Esmaeeli (Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, I.R. Iran.)
Ahmad Erfanian (Department of Pure Mathematics and The Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, Mashhad, I. R. Iran.)
Madjid Mirzavaziri (Department of Pure Mathematics and The Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, Mashhad, I. R. Iran.)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 9, No 1 (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.