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An orientation of a graph G is a digraph D obtained from G by replacing each edge by exactly one of the two possible arcs with the same endvertices. For each v∈V(G), the indegree of v in D, denoted by dD-(v), is the number of arcs with head v in D. An orientation D of G is proper if dD-(u)≠dD-(v), for all uv∈E(G). The proper orientation number of a graph G, denoted by χ→(G), is the minimum of the
