A digraph D in which each of its arcs is coloured by either red or blue is called
two-coloured digraph. A strongly connected of two-coloured digraph is primitive
provided there are nonnegative integers m and b such that for each pair of vertices
u and v in D there is a walk with length m + b, in which m arcs coloured by
red and b arcs coloured by blue. Let D is a two-coloured digraph with V (D)
= {v1, v2, · · · , vn} for each vk 2 V (D), the vertex exponent of D is the smallest
nonnegative integer m + b such that there is a walk with length m + b from vk to
each vertex in D. Let D is a two-coloured digraph on n vertex with n 3 and 2
loops, if vk, k = 1, 2, ..., n is vertex of D, this paper will give the general of vertex
exponent of D exactly 2n−2 for k = 1, 2, 3 and exactly 2n−5+k for 4 k n.
Universitas Sumatera
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