Scrambling Index dari Kelas Digraf Hamilton Dwiwarna dengan n Titik Ganjil

Abstract

ABSTRACT The scrambling index of a primitive two-colored digraph D(2) is the least positive integer h + ℓ over all pairs of nonnegative integers (h, ℓ) such that for each pair of vertices u and v in D(2) there is a vertex w in D(2) with the property that there is an (h, ℓ)-walk from u to w and an (h, ℓ)-walk from v to w. This paper discuss the scrambling index of a class of two-colored Hamiltonian digraph on n ≥ 5 odd vertices consist of two cycles of length n and (n − 1)/2, respectively. First, this paper discuss the primitivity of a two-colored digraph D(2) and then present for mulae for scrambling index that depend on n vertex and the position of the blue arcs relative to the vertex of indegree two. Keywords: Primitive, two-colored digraph, Hamiltonian digraph, scrambling index.