INCOMING LOCAL EXPONENT FOR A TWO-CYCLE BICOLOUR HAMILTONIAN DIGRAPH WITH A DIFFERENCE
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
1 2021
Kata Kunci/Keyword
Abstrak/Abstract
A bicolour digraph is a directed graph with arcs in two colours,
red and black. Let m and h be nonnegative integers representing the number
of red arcs and black arcs, respectively. The incoming local exponent of a
vertex vx on a bicolour digraph is the smallest positive integer m + h over all
pairs of nonnegative integers (m, h) such that for every vertex in vg there is
a walk from vg to vx consisting of m red arcs and h black arcs. We discuss
incoming local exponents for a Hamiltonian bicolour digraph with two cycles
of lengths n and 5n + 1. We also present the primitivity of this digraph, as
well as a formula for the incoming local exponents at its vertices.
