Regular handicap graphs of order n ≡ 4 (mod 8)

Dalibor Froncek, Aaron Shepanik


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, the weight w(xi) is the sum of labels of all neighbors of xi, and the sequence of the weights w(x1),w(x2),…,w(xn) forms an increasing arithmetic progression. A graph G is a handicap distance antimagic graph if it allows a handicap distance antimagic labeling. We construct r-regular handicap distance antimagic graphs of order n ≡ 4 (mod 8) for all feasible values of r.


Graph labeling, handicap labeling, regular graphs, tournament scheduling

Full Text:




S. Arumugam, D. Froncek, and N. Kamatchi, Distance magic graphs – A Survey, ˇ J. Indones. Math. Soc., Special Edition (2011), 11–26.

B. Freyberg, Distance magic type and distance anti-magic-type labelings of Graphs, Ph.D. Thesis, Michigan Technological University, USA (2017).

B. Freyberg, Regular d-handicap graphs of even order, Bull. Inst. Combin. Appl. 83 (2018), 108–117.

D. Froncek, Fair incomplete tournaments with odd number of teams and large number of games, Congr. Numer. 187 (2007), 83–89.

D. Froncek, Handicap distance antimagic graphs and incomplete tournaments, AKCE Int. J. Graphs Comb. 10(2) (2013), 119–127.

D. Froncek, A note on incomplete regular tournaments with handicap two of order n ≡ 8 (mod 16), Opuscula Math. 37(4) (2017), 557–566.

D. Froncek, Full spectrum of regular incomplete 2-handicap tournaments of order n ≡ 0 (mod 16), J. Combin. Math. Combin. Comput., 106 (2018), 175–184.

D. Froncek, Regular handicap graphs of odd order, J. Combin. Math. Combin. Comput., 102 (2017), 253–266.

D. Froncek, P. Kov ˇ a´ˇr and T. Kova´ˇrova, Fair incomplete tournaments, ´ Bull. Inst. Combin.

Appl. 48 (2006), 31–33.

D. Froncek, P. Kov ˇ a´ˇr, T. Kova´ˇrova, B. Krajc, M. Krav ´ cenko, M. Krbe ˇ cek, A. Shepanik ˇand A. Silber, On regular handicap graphs of even order, Electron. Notes Discrete Math. 60 (2017), 69–76.

D. Froncek, A. Shepanik, Regular handicap tournaments of high degree, J. Algebra Comb.

Discrete Appl. 3(3) (2016), 159–164.

D. Froncek, A. Shepanik, Regular handicap graphs of order n ≡ 0 (mod 8), Electron. J. Graph Theory Appl. 6 (2) (2018), 208–218.

J. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. DS 6 (2020).

D. Hoffman and C. Rodger, The chromatic index of complete multipartite graphs, J. Graph Theory 16(2) (1992), 159–163.

P. Kova´ˇr, T. Kova´ˇrova, B. Krajc, M. Krav ´ cenko, M. Krbe ˇ cek, On regular handicap graphs, ˇ unpublished manuscript.

T. Kova´ˇrova, On regular handicap graphs, conference presentation. ´

M. Miller, C. Rodger, and R. Simanjuntak, Distance magic labelings of graphs, Australas. J. Combin. 28 (2003), 305–315.

A. Shepanik, Graph labelings and tournament scheduling, MS Thesis, University of Minnesota Duluth, USA (2015).

G. Stern, H. Lenz, Steiner triple systems with given subspaces; another proof of the DoyenWilson theorem, Boll. Un. Mat. ltal. (5) 17A (1980) 109–114.

V. Vilfred, Sigma-labelled graph and circulant graphs, Ph.D. Thesis, University of Kerala,Trivandrum, India (1994).


  • There are currently no refbacks.

ISSN: 2338-2287

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

View EJGTA Stats