| Abstrak/Abstract |
A digraph that has arcs of two colours is called a
two-coloured digraph. In this case, the colours used are red and
black. Let d and k be non-negative integers, where d represents
the number of red arcs and k represents the number of black
arcs. A (d, k)-walk on the two-coloured digraph is defined as
a walk with d red arcs and k black arcs. The smallest integer
sum of d and k such that there is a (d, k)-walk from vertex
y to vertex z is called the exponent number of two-coloured
digraph, whereas the smallest integer sum of d and k such
that there is (d, k)-walk from each vertex to vertex vx is called
the inner local exponent of a vertex vx. This article discusses
the inner local exponent of a two-cycle non-Hamiltonian twocoloured digraph with cycle lengths n and 3n+ 1. This digraph
has exactly four red arcs. The four red arcs are combined
consecutively or alternately when there is one allied vertex. |
