Journal of the
Korean Mathematical Society JKMS

In this paper, we study a strong $k$-deformation retract derived from a relative $k$-homotopy and investigate its properties in relation to both a $k$-homotopic thinning and the $k$-fundamental group. Moreover, we show that the $k$-fundamental group of a wedge product of closed $k$-curves not $k$-contractible is a free group by the use of some properties of both a strong $k$-deformation retract and a digital covering. Finally, we write an algorithm for calculating the $k$-fundamental group of a closed $k$-curve by the use of a $k$-homotopic thinning.

Keywords: digital image, digital $k$-graph, $(k_0, k_1)$-homeomorphism, $(k_0, k_1)$-isomorphism, strongly local $(k_0,k_1)$-isomorphism, $k$-fundamental group, simple $k$-curve point, simple $k$-point, $k$-thinning algorithm, simply $k$-connected, $k$-homotopy equ

MSC numbers: 55P10, 55P15, 52xx, 55Q70