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Brahim Benmedjdoub, Isma Bouchemakh and Éric Sopena

integer distance graphs , Discrete Math. 191 (1998) 113–123. doi:10.1016/S0012-365X(98)00099-5 [8] F. Kramer and H. Kramer, Un probleme de coloration des sommets d’un graphe , C. R. Acad. Sci. Paris A 268 (1969) 46–48. [9] F. Kramer and H. Kramer, A survey on the distance-colouring of graphs , Discrete Math. 308 (2008) 422–426. doi:10.1016/j.disc.2006.11.059 [10] K.-W. Lih and W.-F. Wang, Coloring the square of an outerplanar graph , Taiwanese J. Math. 10 (2006) 1015–1023. doi:10.11650/twjm/1500403890 [11] D.D.-F. Liu, From rainbow to

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Sylwia Cichacz and Agnieszka Gőrlich

R eferences [1] Y. Alavi, A.J. Boals, G. Chartrand, P. Erdős and O.R. Oellerman, The ascending subgraph decomposition problem , Congr. Numer. 58 (1987) 7–14. [2] K. Ando, S. Gervacio and M. Kano, Disjoint subsets of integers having a constant sum , Discrete Math. 82 (1990) 7–11. doi:10.1016/0012-365X(90)90040-O [3] M. Anholcer and S. Cichacz, Note on distance magic products G ◦ C 4 , Graphs Combin. 31 (2015) 1117–1124. doi:10.1007/s00373-014-1453-x [4] M. Anholcer, S. Cichacz, I. Peterin and A. Tepeh, Distance magic labeling

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Hamzeh Mujahed and Benedek Nagy

modern applications. ninth edition, Pearson Education, Inc.g, New Jersey, 2007. [18] M. Randic, Novel molecular descriptor for structure-property studies, Chemical Physics Letters 211 (1993), 478-483. [19] N. J. A. Sloane (ed.), The On-Line Encyclopedia of Integer Sequences, published electronically at https://oeis.org, time of access: 04.04.2017 [20] R. Strand and B. Nagy, Distances based on neighbourhood sequences in non-standard three-dimensional grids, Discrete Applied Mathematics 155 (2007), 548

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Anshika Srivastava, Ram Krishna Pandey and Om Prakash

REFERENCES [1] CANTOR, D. G.—GORDON, B.: Sequences of integers with missing differences , J. Combin. Theory Ser. A 14 (1973), 281–287. [2] CHANG, G.–LIU, D. D.-F.—ZHU, X.: Distance graphs and T -colorings , J. Combin. Theory Ser. B 75 (1999), 159–169. [3] CIPU, M.—LUCA, F.: On the Galois group of the generalized Fibonacci polynomial , An. Ştiinţ. Univ. Ovidius Constanţa Ser. Mat. 9 (2001), 27–38. [4] COLLISTER, D.—LIU, D. D.-F.: Study of κ ( D ) for D = {2, 3, x , y }, IWOCA (2014), 250–261. [5] GRIGGS, J. R.—LIU, D. D.-F.:, The

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Yota Otachi

(2005) 3-15. [8] Y. Otachi, T. Saitoh, K. Yamanaka, S. Kijima, Y. Okamoto, H. Ono, Y. Uno and K. Yamazaki, Approximability of the path-distance-width for AT-free graphs, Lecture Notes in Comput. Sci., WG 2011 6986 (2011) 271-282. doi:10.1007/978-3-642-25870-1 25 [9] O. Riordan, An ordering on the even discrete torus, SIAM J. Discrete Math. 11 (1998) 110-127. doi:10.1137/S0895480194278234 [10] K. Yamazaki, On approximation intractability of the path-distance-width problem, Discrete Appl. Math. 110 (2001) 317-325. doi:10

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Aloysius Godinho, Tarkeshwar Singh and S. Arumugam

R eferences [1] S. Arumugam, D. Froncek and N. Kamatchi, Distance magic graphs—a survey , J. Indones. Math. Soc. Special Edition (2011) 11–26. doi:10.22342/jims.0.0.15.11-26 [2] A. Godinho, T. Singh and S. Arumugam, On S-magic graphs , Electron. Notes Discrete Math. 48 (2015) 267–273. doi:10.1016/j.endm.2015.05.040 [3] J.A. Gallian, A dynamic survey of graph labeling , Electron. J. Combin. (2014) #DS6. [4] M. Miller, C. Rodger and R. Simanjuntak, Distance magic labelings of graphs , Australas. J. Combin. 28 (2003) 305–315. [5

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Mirka Miller, Joe Ryan and Zdeněk Ryjáček

References [1] J.A. Bondy, U.S.R. Murty, Graph Theory (Springer, NewYork, 2008). doi:10.1007/978-1-84628-970-5 [2] G. Exoo and R. Jajcay, Dynamic cage survey, Electron. J. Combin. 18 (2011) #DS16. [3] F. Lazebnik, V.A. Ustimenko and A.J. Woldar, New upper bounds on the order of cages, Electron. J. Combin. 4(2) (1977) R13. [4] L. Lovász, J. Pelikán and K. Vesztergombi, Discrete Mathematics: Elementary and Beyond (Springer, NewYork, 2003). [5] Z. Ryjáček, N2-locally

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Daouya Laïche, Isma Bouchemakh and Éric Sopena

.1016/j.dam.2012.08.008 [4] B. Brešar, S. Klavžar and D.F. Rall, On the packing chromatic number of Cartesian products, hexagonal lattice, and trees , Discrete Appl. Math. 155 (2007) 2303–2311. doi:10.1016/j.dam.2007.06.008 [5] J. Ekstein, J. Fiala, P. Holub and B. Lidický, The packing chromatic number of the square lattice is at least 12, March 12, 2010. arXiv:1003.2291v1 [cs.DM]. [6] J. Ekstein, P. Holub and B. Lidický, Packing chromatic number of distance graphs , Discrete Appl. Math. 160 (2012) 518–524. doi:10.1016/j.dam.2011

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Sylwia Cichacz, Bryan Freyberg and Dalibor Froncek

R eferences [1] S. Arumugam, D. Froncek and N. Kamatchi, Distance Magic Graphs—A Survey , J. Indones. Math. Soc., Special Edition (2011) 11–26. doi:10.22342/jims.0.0.15.11-26 [2] G.S. Bloom and D.F. Hsu, On graceful digraphs and a problem in network addressing , Congr. Numer. 35 (1982) 91–103. [3] G.S. Bloom, A. Marr and W.D. Wallis, Magic digraphs , J. Combin. Math. Combin. Comput. 65 (2008) 205–212. [4] S. Cichacz, Note on group distance magic graphs G [ C 4 ], Graphs Combin. 30 (2014) 565–571. doi:10.1007/s00373-013-1294-z

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Hamideh Aram, Sepideh Norouzian and Seyed Mahmoud Sheikholeslami

References [1] J.A. Bondy, U.S.R. Murty, Graph Theory with Applications (The Macmillan Press Ltd. London and Basingstoke, 1976). [2] E.W. Chambers, B. Kinnersley, N. Prince and D.B. West, Extremal problems for Roman domination, SIAM J. Discrete Math. 23 (2009) 1575-1586. doi:10.1137/070699688 [3] E.J. Cockayne, P.M. Dreyer Jr., S.M. Hedetniemi and S.T. Hedetniemi, On Roman domination in graphs, Discrete Math. 278 (2004) 11-22. doi:10.1016/j.disc.2003.06.004 [4] E.J. Cockayne, P