Vertex-Magic Total Labeling Algorithms on Unicycle Graphs and Some Graphs Related to Wheels
Abstract: Let G be a graph
with vertex set V and edge set E, where |V| and |E| be the number of vertices
and edges of G. A bijection λ : V E {1, 2, …, |V| + |E|} is called a
vertex-magic total labeling if there is a constant k so that the weight of
vertex x, wλ(x) = λ(x) + yN(x) λ(xy) = k, for all x in V where N(x) is the
set of vertices adjacent to x. This paper gives algorithms to generate all
vertex-magic total labelings on some
classes of unicycle graphs (suns and tadpoles) and some classes of graph
related to wheels (friendships, fans,
generalized Jahangirs). Using those algorithms, we enumerate all non isomorphic
vertex-magic total labelings on those classes of graphs for some values of
|V|.
Keywords: Fan, Friendship,
Generalized Jahangir, Sun, Tadpole, Unicycle, Vertex magic total labeling,
Wheel
Author: Denny Riama Silaban,
Budi Utami, Alfa Isti Ananda, Dhian Widya, and Siti Aminah
Journal Code: jpmatematikagg120001
