On very sparse circulant (0, 1) matrices

In this paper a particular partition on blocks of generalized circulant (0, 1) matrices of composite order, with three ones per row, is determined. Using this result it is shown that the bipartite graph, associated with a similar matrix in the usual way, has genus 1, but a particular case, where it holds 0. Moreover a lower bound for the permanent of these matrices is achieved.