TY - JOUR

T1 - Vertex-Magic Total Labeling Algorithms on Unicycle Graphs and Some Graphs Related to Wheels

AU - Silaban, Denny Riama

AU - Utami, Budi

AU - Ananda, Alfa Isti

AU - Widya, Dhian

AU - Aminah, Siti

PY - 2012

Y1 - 2012

N2 - 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 È 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) + åyÎN(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|.

AB - 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 È 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) + åyÎN(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|.

UR - https://journal.fmipa.itb.ac.id/jms/article/view/366

M3 - Article

JO - Jurnal Matematika dan Sains (e-Journal)

JF - Jurnal Matematika dan Sains (e-Journal)

SN - 2442-7349

ER -