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Universal Journal of Applied Mathematics Vol. 2(6), pp. 250 - 255
DOI: 10.13189/ujam.2014.020603
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The Scrambling Index of Two-colored Wielandt Digraph

Mulyono , Saib Suwilo ^*
Department of Mathematics, University of Sumatera Utara, Medan 20155 Indonesia

ABSTRACT

A digraph is primitive provided there is a positive integer k such that for each pair of vertices u and v there exist walks of length k from u to v and from v to u. The scrambling index of a primitive digraph D is the smallest positive integer k such that for each pair of vertices u and v in D there is a vertex w such that there exist walks of length k from u to w and from v to w . A two-colored digraph is a digraph each of whose arc is colored by red or blue. In this paper we generalize the notion of scrambling index of a primitive digraph to that of two-colored digraph. We define the scrambling index of a two-colored digraph D⁽²⁾ to be the smallest positive integer h + 鈩� over all pairs of nonnegative integers (h, 鈩�) such that for each pair of distinct vertices u and v there is a vertex w with the property that there are walks form u to w and from v to w consisting of h red arcs and 鈩� blue arcs. For two-colored Wielandt digraph on n 鈮� 4 vertices we show the scrambling index lies on the interval [n²锛�3n + 3, n²锛�2苍+2闭.

KEYWORDS
Two-colored Digraph, Primitive Digraph, Scrambling Index, Wielandt Digraph

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Mulyono , Saib Suwilo , "The Scrambling Index of Two-colored Wielandt Digraph," Universal Journal of Applied Mathematics, Vol. 2, No. 6, pp. 250 - 255, 2014. DOI: 10.13189/ujam.2014.020603.

(b). APA Format:
Mulyono , Saib Suwilo (2014). The Scrambling Index of Two-colored Wielandt Digraph. Universal Journal of Applied Mathematics, 2(6), 250 - 255. DOI: 10.13189/ujam.2014.020603.