Fibonacci numbers in graphs with strong (1,1,2)-kernels

摘要

In this paper, we study strong (1, 1, 2)-kernels in graphs which generalize classical kernels, (1, 2)-kernels and 2-dominating kernels, simultaneously. We give a complete characterization of trees with a strong (1, 1, 2)-kernel. Moreover, we present some realization theorems and show connections between the number of strong (1, 1, 2)-kernels and Fibonacci and Lucas numbers.