TY - JOUR

T1 - Vertex magic total labelings of 2-regular graphs

AU - Cichacz, Sylwia

AU - Froncek, Dalibor

AU - Singgih, Inne

N1 - Publisher Copyright:
© 2016 Elsevier Ltd

PY - 2017/1/6

Y1 - 2017/1/6

N2 - A vertex magic total (VMT) labeling of a graph G = ( V, E ) is a bijection from the set of vertices and edges to the set of integers defined by λ : V ∪ E → { 1, 2, …, | V | + | E | } so that for every x ∈ V, w ( x ) = λ ( x ) + ∑ x y ∈ E λ ( x y ) = k, for some integer k. A VMT labeling is said to be a super VMT labeling if the vertices are labeled with the smallest possible integers, 1, 2, …, | V |. In this paper we introduce a new method to expand some known VMT labelings of 2-regular graphs.

AB - A vertex magic total (VMT) labeling of a graph G = ( V, E ) is a bijection from the set of vertices and edges to the set of integers defined by λ : V ∪ E → { 1, 2, …, | V | + | E | } so that for every x ∈ V, w ( x ) = λ ( x ) + ∑ x y ∈ E λ ( x y ) = k, for some integer k. A VMT labeling is said to be a super VMT labeling if the vertices are labeled with the smallest possible integers, 1, 2, …, | V |. In this paper we introduce a new method to expand some known VMT labelings of 2-regular graphs.

KW - Magic-type labelings

KW - Vertex magic total labelings

UR - http://www.scopus.com/inward/record.url?scp=84982684398&partnerID=8YFLogxK

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U2 - 10.1016/j.disc.2016.06.022

DO - 10.1016/j.disc.2016.06.022

M3 - Article

AN - SCOPUS:84982684398

SN - 0012-365X

VL - 340

SP - 3117

EP - 3124

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1

ER -