THE SCRAMBLING INDEX OF TWO-COLORED WIELANDT DIGRAPH

Mulyono, and Suwilo, Saib (2014) THE SCRAMBLING INDEX OF TWO-COLORED WIELANDT DIGRAPH. Universal Journal of Applied Mathematics, 2 (6). pp. 250-255. ISSN 2331-6446

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Official URL: http://www.hrpub.org/download/20140525/UJAM3-12602...

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 + ℓ over all pairs of nonnegative integers (h, ℓ) 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 ℓ blue arcs. For two-colored Wielandt digraph on n ≥ 4 vertices we show the scrambling index lies on the interval [n2 − 3n + 3, n2 − 2n + 2].

Item Type: Article
Keywords: Two-colored digraph, Primitive digraph, Scrambling Index, Wielandt digraph
Subjects: Q Science > QA Mathematics
Divisions: Fakultas Matematika dan Ilmu Pengetahuan Alam > Matematika
Depositing User: Mrs Gusti Lisa Utami
Date Deposited: 22 May 2018 03:48
URI: http://digilib.unimed.ac.id/id/eprint/30407

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