Open AccessVk- Super Vertex In-Magic Labelings of Directed Graphs
Author(s) -
Sivagnanam Mutharasu,
Nicolas Bernard,
D. Senthil Kumar
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1850/1/012067
Subject(s) - algorithm , magic (telescope) , vertex (graph theory) , physics , combinatorics , mathematics , graph , quantum mechanics
Let D be a digraph of order p and size q . For an integer k ⩾ 1 and ν ∈ V ( D ), let ∑ e ∈ E k ( v ) f ( e ) where E k ( v ) is the set of all in-arcs which are at distance at most k from ν . A V k -super vertex in-magic labeling ( V k -SVIML) 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 for every ν ∈ V ( D ), f ( ν ) + ω k ( ν ) = M for some positive integer M. A digraph that admits a V k -SVIML is called V k -super vertex in-magic ( V k -SVIM). In this paper, we study some properties of V k -SVIML in digraphs. We characterized the digraphs which are V k -SVIM. Also, we find the magic constant for E k -regular digraphs. Farther, we characterized the unidirectional cycles and union of unidirectional cycles which are V 2 -SMM.