On the In-Out-Proper Orientations of Graphs

2021/06/24 by Dehghan, Ali
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2106.13357

Abstract

An orientation of a graph G is \it in-out-proper if any two adjacent vertices have different in-out-degrees, where the in-out-degree of each vertex is equal to the in-degree minus the out-degree of that vertex. The \it in-out-proper orientation number of a graph G, denoted by \overleftrightarrowχ(G), is min_{D∈ Γ}max_{v∈ V(G)} |d_D^±(v)|, where Γ is the set of in-out-proper orientations of G and d_D^±(v) is the in-out-degree of the vertex v in the orientation D.

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