in [2], Choi constructs a bijection between the set of Davis-Januszkiewicz equivalence classes of small covers over an n-cube and the set of acyclic
digraphs with n-labeled nodes.
Example 7 Consider the SVN
digraph [mathematical expression not reproducible] in Figure 1 with vertex set [mathematical expression not reproducible] and arc set [mathematical expression not reproducible] with one loop at each vertex as follows:
Let
digraph (G, A) be strongly connected, in which A = [([[delta].sub.kh]).sub.lxl].
(ii) The
digraph G = (V, E) is said to be transitive if whenever (x, y) [member of] E and (y, z) [member of] E, (x, z) [member of] E.
Jia, "Interval bipartite consensus of networked agents associated with signed
digraphs," Institute of Electrical and Electronics Engineers Transactions on Automatic Control, vol.
where each [G.sub.i] is a
digraph. We need this fact and the following lemmas.
In Section 4, the existence of a common N-tupled fixed point of operators satisfying ([phi], [psi])-contractive conditions in metric spaces endowed with a
digraph is considered.
By induction, there exists
digraph isomorphism [[phi].sub.i] : T([a.sub.i]) [right arrow] T([b.sub.i]).
The adjancency matrixA(D) of a
digraph D is the p x p matrix [[a.sub.ij]] with [a.sub.ij] = 1 if [v.sub.i][v.sub.j] is an arc of D, and 0 otherwise (Fig.
If the
digraph G has a spanning tree, then its Laplacian matrix L has a simple zero eigenvalue and all other eigenvalues have positive real parts.