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On k-independent sets and (k, l)-kernels in the corona of graphs

Szumny W., Włoch A.

Journal of Mathematics and Applications

2007

Vol. 29

127-135

A subset S ⊆ V(G) is a k-independent set if no two of its vertices are in distance less than k. In this paper we study fc-independent sets and (k, l)-kernels (i.e. k-independent sets being l-dominating simultaneously) in the corona of graphs. We describe an arbitrary k-independent set of the corona and next we determine the Fibonacci number and the generalized Fibonacci number of the corona of special graphs. We give the necessary and sufficient conditions for the existence of (k, l)-kernels in the corona.