On regular handicap graphs of even order

Citation data:

Electronic Notes in Discrete Mathematics, ISSN: 1571-0653, Vol: 60, Page: 69-76

Publication Year:
2017
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DOI:
10.1016/j.endm.2017.06.010
Author(s):
Dalibor Fronček; Petr Kovář; Tereza Kovářová; Bohumil Krajc; Michal Kravčenko; Aaron Shepanik; Adam Silber
Publisher(s):
Elsevier BV
Tags:
Mathematics
article description
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.