### Minimum Feedback Vertex Sets in Distance Graphs and Circulant Graphs

*Hamamache Kheddouci, Olivier Togni*

#### Abstract

For a set D⊂Z

_{n}, the distance graph P_{n}(D) has Z_{n}as its vertex set and the edges are between vertices i and j with |i-j|∈D. The circulant graph C_{n}(D) is defined analogously by considering operations modulo n. The minimum feedback vertex set problem consists in finding the smallest number of vertices to be removed in order to cut all cycles in the graph. This paper studies the minimum feedback vertex set problem for some families of distance graphs and circulant graphs depending on the value of D.Full Text: PDF PostScript