Abstract
A two-colored digraph is a digraph for which each of its arc is colored by red or blue. An (h, ℓ)-walk is a walk consisting of h red arcs and ℓ blue arcs. A strongly connected two-colored digraph is primitive provided there exist nonnegative integers h and ℓ such that for each ordered pair of vertices u and v there is a(h, ℓ)-walk from u to v. The local exponent of a vertex v in a primitive two-colored digraph D(2), denoted by exp(v, D(2)) is the least positive integer h + ℓ over all nonnegative integers h and ℓ such that for vertex u in D(2) there is an (h, ℓ)-walk from u to v. We discuss local exponent of primitive two-colored Hamiltonian digraph on n vertices consisting of two cycles of lengths n and n − 3, respectively. For each vertex v in , we present an explicit formula for exp(v, ).
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More From: IOP Conference Series: Materials Science and Engineering
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