Lower and upper orientable strong diameters of graphs satisfying the Ore condition

Let DD be a strong digraph. The strong distance between two vertices uu and vv in DD, denoted by sdD(u,v)sdD(u,v), is the minimum size (the number of arcs) of a strong sub-digraph of DD containing uu and vv. For a vertex vv of DD, the strong eccentricity se(v)se(v) is the strong distance between vv and a vertex farthest from vv. The minimum strong eccentricity among all vertices of DD is the strong radius, denoted by srad(D)srad(D), and the maximum strong eccentricity is the strong diameter, denoted by sdiam(D)sdiam(D). The lower (resp. upper) orientable strong radius srad(G)srad(G) (resp. SRAD(G)SRAD(G)) of a graph GG is the minimum (resp. maximum) strong radius over all strong orientations of GG. The lower (resp. upper) orientable strong diameter sdiam(G)sdiam(G) (resp. SDIAM(G)SDIAM(G)) of a graph GG is the minimum (resp. maximum) strong diameter over all strong orientations of GG. In this work, we determine a bound of the lower orientable strong diameters and the bounds of the upper orientable strong diameters for graphs G=(V,E)G=(V,E) satisfying the Ore condition (that is, σ2(G)=min{d(x)+d(y)|∀xy∉E(G)}≥n), in terms of girth gg and order nn of GG.