The scrambling index of a two-colored digraph is the least positive integer h + over all pairs of nonnegative integers (h, ) such that for each pair of vertices u and v there is a vertex w with the property that there exist a walk from u to w and a walk from v to w that consist of h red arcs and blue arcs. We discuss the scrambling index of a class of two-colored Hamiltonian digraphs on n ≥ 5 odd vertices with two cycles of length n and (n − 1)/2, respectively. We present formulae for scrambling index of such two-colored Hamiltonian digraph that depend on n and the position of the blue arcs relative to the vertex of indegree 2.

1.
M.
Akelbek
and
S.
Kirkland
,
Linear Algebra Appl.
430
(
4
),
1111
1130
(
2009
).
2.
Mulyono
,
H.
Sumardi
, and
S.
Suwilo
,
Far East J. Math. Sci.
96
(
1
),
113
132
(
2015
).
3.
Y.
Gao
and
Y.
Shao
,
Linear Algebra Appl
.
407
,
263
276
(
2005
).
4.
B. L.
Shader
and
S.
Suwilo
,
Linear Algebra Appl
.
363
,
275
293
(
2003
).
5.
S.
Suwilo
,
AIP Conf. Proc.
1450
,
297
(
2012
).
6.
E.
Fornasini
and
M. E.
Valcher
,
SIAM J. Matrix Anal. Appl.
,
19
,
71
88
(
1998
).
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