On regular handicap graphs of even order

Dalibor Fronček; Petr Kovář; Tereza Kovářová; Bohumil Krajc; Michal Kravčenko; Aaron Shepanik; Adam Silber

doi:10.1016/j.endm.2017.06.010

On regular handicap graphs of even order

Dalibor Fronček, Petr Kovář, Tereza Kovářová, Bohumil Krajc, Michal Kravčenko, Aaron Shepanik, Adam Silber

Mathematics & Statistics

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5 Scopus citations

Abstract

Let G=(V,E) be a simple graph of order n. A bijection f : V→{1,2,…,n} is a handicap labeling of G if there exists an integer ℓ such that ∑_u∈N(v)f(u)=ℓ+f(v) for all v∈V, where N(v) is the set of all vertices adjacent to v. Any graph which admits a handicap labeling is a handicap graph. We present an overview of results, which completely answer the question of existence of regular handicap graphs of even order.

Original language	English (US)
Pages (from-to)	69-76
Number of pages	8
Journal	Electronic Notes in Discrete Mathematics
Volume	60
DOIs	https://doi.org/10.1016/j.endm.2017.06.010
State	Published - Jul 2017

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Publisher Copyright:
© 2017 Elsevier B.V.

Keywords

Graph labeling
handicap labeling
regular graphs

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AU - Fronček, Dalibor

AU - Kovář, Petr

AU - Kovářová, Tereza

AU - Krajc, Bohumil

AU - Kravčenko, Michal

AU - Shepanik, Aaron

AU - Silber, Adam

PY - 2017/7

Y1 - 2017/7

N2 - Let G=(V,E) be a simple graph of order n. A bijection f : V→{1,2,…,n} is a handicap labeling of G if there exists an integer ℓ such that ∑u∈N(v)f(u)=ℓ+f(v) for all v∈V, where N(v) is the set of all vertices adjacent to v. Any graph which admits a handicap labeling is a handicap graph. We present an overview of results, which completely answer the question of existence of regular handicap graphs of even order.

AB - Let G=(V,E) be a simple graph of order n. A bijection f : V→{1,2,…,n} is a handicap labeling of G if there exists an integer ℓ such that ∑u∈N(v)f(u)=ℓ+f(v) for all v∈V, where N(v) is the set of all vertices adjacent to v. Any graph which admits a handicap labeling is a handicap graph. We present an overview of results, which completely answer the question of existence of regular handicap graphs of even order.

KW - Graph labeling

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KW - regular graphs

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JO - Electronic Notes in Discrete Mathematics

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ER -

On regular handicap graphs of even order

Abstract

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