TY - JOUR

T1 - A note on incomplete regular tournaments with handicap two of order n ≡ 8 (mod 16)

AU - Froncek, Dalibor

N1 - Publisher Copyright:
© Wydawnictwa AGH, 2017.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2017

Y1 - 2017

N2 - A d-handicap distance antimagic labeling of a graph G = (V, E) with n vertices is a bijection f : V → {1, 2, . . . , n} with the property that f(xi) = i and the sequence of weights w(x1), w(x2), . . . , w(xn) (where w(xi) = ∑xixj∈E f(xj)) forms an increasing arithmetic progression with common difference d. A graph G is a d-handicap distance antimagic graph if it allows a d-handicap distance antimagic labeling. We construct a class of k-regular 2-handicap distance antimagic graphs for every order n ≡ 8 (mod 16), n ≥ 56 and 6 ≤ k ≤ n - 50.

AB - A d-handicap distance antimagic labeling of a graph G = (V, E) with n vertices is a bijection f : V → {1, 2, . . . , n} with the property that f(xi) = i and the sequence of weights w(x1), w(x2), . . . , w(xn) (where w(xi) = ∑xixj∈E f(xj)) forms an increasing arithmetic progression with common difference d. A graph G is a d-handicap distance antimagic graph if it allows a d-handicap distance antimagic labeling. We construct a class of k-regular 2-handicap distance antimagic graphs for every order n ≡ 8 (mod 16), n ≥ 56 and 6 ≤ k ≤ n - 50.

KW - Distance magic labeling

KW - Handicap labeling.

KW - Handicap tournaments

KW - Incomplete tournaments

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U2 - 10.7494/OpMath.2017.37.4.557

DO - 10.7494/OpMath.2017.37.4.557

M3 - Article

AN - SCOPUS:85019472996

VL - 37

SP - 557

EP - 566

JO - Opuscula Mathematica

JF - Opuscula Mathematica

SN - 1232-9274

IS - 4

ER -