Inner Local Exponent of Two-coloured Digraphs with Two Cycles of Length n and 4n + 1
Penulis/Author
YOGO DWI PRASETYO (1); Prof. Dr. Sri Wahyuni, S.U. (2); Yeni Susanti (3); Dr. Diah Junia Eksi Palupi, S.U. (4)
Tanggal/Date
2023
Kata Kunci/Keyword
Abstrak/Abstract
A two-coloured digraph D
(2) is a digraph in which
each arc is coloured with one of two colours – for example, red
or black. A two-coloured digraph D
(2) is said to be primitive
if there are positive integers a and i such that for each pair
of points x and y in D
(2) there is an (a, i)-walk from x to
y. The inner local exponent of a point pv in D
(2) denoted by
expin(pv, D
(2)) is the smallest positive integer a + i over all
non-negative integers a and i such that there is a walk from
each vertex in D
(2) to pv consisting of a red arcs and i black
arcs. In a two-coloured primitive digraph, two cycles of length
n and 4n+1 result in four or five red arcs. For the two-coloured
digraphs, primitivity and inner local exponent are discussed at
each point.
