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Let D(V, A) be a digraph of order p and size q. For an integer k ≥ 1 and for v ∈ V (D), let wk(v) = P
e∈Ek(v)
f(e), where Ek(v)
is the set containing all arcs which are at distance at most k from v.
The digraph D is said to be Ek-regular with regularity r if and only if
|Ek(e)| = r for some integer r ≥ 1 and for all e ∈ A(D). A Vk-super
vertex out-magic labeling (Vk-SVOML) is an one-to-one onto function
f : V (D)∪A(D) → {1, 2, . . . , p+q} such that f(V (D)) = {1, 2, . . . , p}
and there exists a positive integer M such that f(v) + wk(v) = M,
∀ v ∈ V (D). A digraph that admits a Vk-SVOML is called Vk-super
vertex out-magic (Vk-SVOM). This paper contains several properties of
Vk-SVOML in digraphs. We characterized the digraphs which are VkSVOM. Also, the magic constant for Ek-regular graphs has been obtained.
Further, we characterized the unidirectional cycles and union of unidirectional cycles which are V2-SVOM
Sivagnanam Mutharasu, Duraisamy Kumar, N. Mary Bernard. (2019) Vk- Super Vertex Out-Magic Labeling of Digraphs, Punjab University Journal of Mathematics, Volume 51, Issue 7.
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