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PJ Couch, B.D. Daniel, R. Guidry and W. Paul Wright

References [1] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (American Elsevier, New York, 1976). [2] H.J. Broersma, A.J.W. Duijvestijn and F. Gőbel, Generating all 3- connected 4- regular planar graphs from the octahedron graph , J. Graph Theory 17 (1993) 613–620. doi:10.1002/jgt.3190170508 [3] J. Czap and S. Jendrol’, Colouring vertices of plane graphs under restrictions given by faces , Discuss. Math. Graph Theory 29 (2009) 521–543. doi:10.7151/dmgt.1462 [4] N. Dean, Which graphs are pancyclic modulo k? , in

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Zahra Barati and Mojgan Afkhami

(2002) 73–78. [19] A.V. Kelarev, Ring Constructions and Applications (World Scientific, River Edge, NJ, 2002). [20] A.V. Kelarev, Labelled Cayley graphs and minimal automata , Australasian J. Combinatorics 30 (2004) 95–101. [21] A.V. Kelarev, On Cayley graphs of inverse semigroups , Semigroup Forum 72 (2006) 411–418. doi:10.1007/s00233-005-0526-9 [22] A.V. Kelarev and C.E. Praeger, On transitive Cayley graphs of groups and semigroups , European J. Combinatorics 24 (2003) 59–72. doi:10.1016/S0195-6698(02)00120-8 [23] A.V. Kelarev

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Zhangdong Ouyang

R eferences [1] G. Chartrand and L. Lesniak, Graphs and Digraphs, 3rd Edition (Chapman & Hall, New York, 1996). [2] G.L. Chia and C.S. Gan, On crossing numbers of 5 -regular graphs , in: J.-Y. Cai and C.K. Wong (Eds.), Computing and Combinatorics, Lecture Notes in Comput. Sci. 2387 (2002) 230–237. doi:10.1007/3-540-45655-4_26 [3] G.L. Chia and C.S. Gan, Minimal regular graphs with given girths and crossing numbers , Discuss. Math. Graph Theory 24 (2004) 223–237. doi:10.7151/dmgt.1227 [4] Z.D. Ouyang, J. Wang and Y.Q. Huang, The

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Walter Carballosa, Ruy Fabila-Monroy, Jesús Leaños and Luis Manuel Rivera

-Peñaloza, C. Huemer, F. Hurtado, J. Urrutia and D.R. Wood, Token graphs , Graphs Combin. 28 (2012) 365–380. doi:10.1007/s00373-011-1055-9 [5] R. Graham and N. Sloane, Lower bounds for constant weight codes , IEEE Trans. Inform. Theory 26 (1980) 37–43. doi:10.1109/TIT.1980.1056141 [6] J. Guo, K. Wang and F. Li, Metric dimension of some distance-regular graphs , J. Comb. Optim. 26 (2013) 190–197. doi:10.1007/s10878-012-9459-x [7] F. Harary, Graph Theory (Addison-Wesley, Reading, MA, 1969). [8] K. Kuratowski, Sur le problème des courbes

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Zhang Dong Ouyang, Jing Wang and Yuan Qiu Huang

crossing number of K 5, n , J. Combin. Theory Ser. B 9 (1970) 315–323. doi:10.1016/S0021-9800(70)80087-4 [6] M. Klešč, The join of graphs and crossing numbers , Electron. Notes Discrete Math. 28 (2007) 349–355. doi:10.1016/j.endm.2007.01.049 [7] L. Tang, J. Wang and Y.Q. Huang, The crossing number of the join of C m and P n , Internat. J. Math. Com. 1 (2007) 110–116. [8] M. Klešč and S. Schrötter, The crossing numbers of join products of paths with graphs of order four , Discuss. Math. Graph Theory 31 (2011) 321–331. doi:10.7151/dmgt.1548

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Stanislav Jendroľ and Lucia Kekeňáková

R eferences [1] O. Amini, L. Esperet and J. van den Heuvel, A unified approach to distance-two colouring of planar graphs , in: Proc. SODA 2009 273–282. doi:10.1137/1.9781611973068.31 [2] K. Appel and W. Haken, Every planar graph is four colorable, Part I : Discharging , Illinois J. Math. 21 (1977) 429–490. [3] K. Appel and W. Haken, Every planar graph is four colorable, Part II : Reducibility , Illinois J. Math. 21 (1977) 491–567. [4] J. Azarija, R. Erman, D. Kráľ, M. Krnc and L. Stacho, Cyclic colorings of plane graphs with

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Lingping Zhong

R eferences [1] C. Betancur, R. Cruz and J. Rada, Vertex-degree-based topological indices over star-like trees , Discrete Appl. Math. 185 (2015) 18–25. doi:10.1016/j.dam.2014.12.021 [2] H. Deng, S. Balachandran and S.K. Ayyaswamy, On two conjectures of Randić index and the largest signless Laplacian eigenvalue of graphs , J. Math. Anal. Appl. 411 (2014) 196–200. doi:10.1016/j.jmaa.2013.09.014 [3] H. Deng, S. Balachandran, S.K. Ayyaswamy and Y.B. Venkatakrishnan, On the harmonic index and the chromatic number of a graph , Discrete Appl

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Zongpeng Ding and Yuanqiu Huang

R eferences [1] K. Asano, The crossing number of K 1 , 3 ,n and K 2 , 3 ,n , J. Graph Theory 10 (1986) 1–8. doi:10.1002/jgt.3190100102 [2] J.A. Bondy, U.S.R. Murty, Graph Theory with Applications (North-Holland, New York-Amsterdam-Oxford, 1982). [3] P. Erdős and R.K. Guy, Crossing number problems , Amer. Math. Monthly 80 (1973) 52–58. doi:10.2307/2319261 [4] P.T. Ho, On the crossing number of K 1 ,m,n , Discrete Math. 308 (2008) 5996–6002. doi:10.1016/j.disc.2007.11.023 [5] Y. Huang and T. Zhao, The crossing number of K 1

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Stanislav Jendrol’, Mirko Horňák and Roman Soták

: 10.1002/jgt.3190140108 [15] N. Robertson, D. Sanders, P. Seymour and R. Thomas, The four-colour theorem, J. Combin. Theory Ser. B 70 (1997) 2-44. doi: 10.1006/jctb.1997.1750 [16] W.C. Shiu, P.C.B. Lam and D.L. Chen, On incidence coloring for some cubic graphs, Discrete Math. 252 (2002) 259-266. doi: 10.1016/S0012-365X(01)00457-5 [17] W.C. Shiu and P.K. Sun, Invalid proofs on incidence coloring, Discrete Math. 308 (2008) 6575-6580. doi: 10.1016/j.disc.2007.11.030 [18] P.K. Sun, Incidence coloring of

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Július Czap, Peter Šugerek, Stanislav Jendrol’ and Juraj Valiska

.1016/j.disc.2008.09.021 [9] I. Fabrici, S. Jendrol’ and M. Vrbjarová, Unique-maximum edge-colouring of plane graphs with respect to faces , Discrete Appl. Math. 185 (2015) 239–243. doi:10.1016/j.dam.2014.12.002 [10] I. Fabrici, S. Jendrol’ and M. Vrbjarová, Facial entire colourings of plane graphs , Discrete Math. 339 (2016) 626–631. doi:10.1016/j.disc.2015.09.011 [11] I. Fabrici, S. Jendrol’ and M. Voigt, Facial list colourings of plane graphs , Discrete Math. 339 (2016) 2826–2831. doi:10.1016/j.disc.2016.05.034 [12] H. Grötzsch, Ein