Forced Orientation of Graphs

forced orientation of graphs

Forced orientation of graphs

The concept of forced orientation of graphs was introduced by G. Chartrand et al. in 1994. If, for a given assignment of directions to a subset S of the edges of a graph G, there exists an orientation of E(G) \ S, so that the resulting graph is strongly connected, then that given assignment is said to be extendible to a strong orientation of G. The forced strong orientation number fD(G), with r...

Orientation distance graphs revisited

The orientation distance graph Do(G) of a graph G is defined as the graph whose vertex set is the pair-wise non-isomorphic orientations of G, and two orientations are adjacent iff the reversal of one edge in one orientation produces the other. Orientation distance graphs was introduced by Chartrand et al. in 2001. We provide new results about orientation distance graphs and simpler proofs to ex...

Unilateral Orientation of Mixed Graphs

A digraph D is unilateral if for every pair x, y of its vertices there exists a directed path from x to y, or a directed path from y to x, or both. A mixed graph M = (V,A,E) with arc-set A and edgeset E accepts a unilateral orientation, if its edges can be oriented so that the resulting digraph is unilateral. In this paper, we present the first linear-time recognition algorithm for unilaterally...

Encoding Orientation of Graphs by Vertex Labels

Let E = (V;A) be an antisymmetric directed graph, the elements of V being called labels. We say that the orientation of a directed (simple, loopless) graph H = (V;A) can be encoded by E if there exists a mapping : V ! V satisfying : 8 (x; y) 2 A; ( (x); (y)) 2 A. It has been proved that the orientation of any directed planar (resp. outerplanar, with maximal degree 3) graph can be encoded by usi...

Antimagic Orientation of Biregular Bipartite Graphs

An antimagic labeling of a directed graph D with n vertices and m arcs is a bijection from the set of arcs of D to the integers {1, . . . ,m} such that all n oriented vertex sums are pairwise distinct, where an oriented vertex sum is the sum of labels of all arcs entering that vertex minus the sum of labels of all arcs leaving it. An undirected graph G is said to have an antimagic orientation i...