THE ORIENTABLE NUMBERS OF A GRAPH

Abstract

For a connected graph G, there are orientations of G have different hull numbers, geodetic numbers, and convexity numbers. The lower orientable hull number h (G) is defined as the minimum hull num- ber among all the orientations of G and the upper orientable hull number h + (G) as the maximum hull number among all the orientations of G. The lower and upper orientable geodetic numbers g (G) and g + (G) are defined similarily. In this paper, We investigate characterizations of the orientable numbers and the conditions that the relation h (G) g (G) < h + (G) g + (G) holds.