Abstract
We construct Hamilton cycles in connected loopless circulant digraphs of outdegree three with connection set of the form for an integer satisfying the condition for some integer such that , where . This extends work of Miklavi and ?parl, who previously deter-mined the Hamiltonicity of these digraphs in the case where and , to other values of which depend on the generators and .
Highlights
C and Šparl, who previously determined the Hamiltonicity of these digraphs in the case where k 1 and k 2, to other values of k which depend on the generators a and b
For elements a1, a2, am of n, the symbol a1, a2, am denotes the subgroup of n generated by the elements a1, a2, am, which is comprised of all linear combinations of the elements For an element a n, the set a1, a2, am b x: x
A digraph is a pair V, A in which V is a set of vertices and A is a set of ordered pairs of elements of
Summary
The group of integers under the operation of addition modulo n is denoted by n. A subset S of n is a generating set for n if every element of n can be written as a linear combination of elements in S. For elements a1, a2 , , am of n , the symbol a1, a2 , , am denotes the subgroup of n generated by the elements a1, a2 , , am , which is comprised of all linear combinations of the elements For an element a n , the set a1, a2 , , am b x: x in a n . Circ n; S is the digraph with vertex set n and arcs from v to v s for all v n and all s S. The set S is called the connection set of the digraph. The circulant digraph Circ n; S is connected if and only if S is a generating set for n.
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