References
- S. Arumugam, K.R. Chandrasekar, N. Misra, et al., Algorithmic aspects of dominator colorings in graphs, Combinatorial Algorithms. Springer Berlin Heidelberg, (2011) 19–30.
- B. Bollobás, Chromatic number, girth and maximal degree, Discrete Mathematics, 24(3)(1978) 311–314. doi: 10.1016/0012-365X(78)90102-4
- M. Chellali, F. Maffray, Dominator colorings in some classes of graphs, Graphs and Combinatorics 28(1) (2012) 97–107. doi: 10.1007/s00373-010-1012-z
- T.T. Chelvam, I. Rani, Dominating sets in Cayley graphs on Zn, Tamkang Journal of Mathematics 38(4) (2007) 341–345. doi: 10.5556/j.tkjm.38.2007.68
- T.T. Chelvam, I. Rani, Total and connected domination numbers for Cayley graphs on Zn, Advanced Studies in Contemporary Mathematics 20 (2010) 57–61.
- L. Chen, H. Jiang, Z. Shao, et al., Dominator and total dominator colorings in vague graphs, Engineering and Applied Science Letters 2 (2019) 10–17. doi: 10.30538/psrp-easl2019.0017
- Q. Chen, C. Zhao and M. Zhao, Dominator colorings of certain cartesian products of paths and cycles, Graphs and Combinatorics 33(1) (2017) 73–83. doi: 10.1007/s00373-016-1742-7
- B. Codenotti, I. Gerace, S. Vigna, Hardness results and spectral techniques for combinatorial problems on circulant graphs, Linear Algebra and its Applications 285(1) (1998) 123–142. doi: 10.1016/S0024-3795(98)10126-X
- R. Gera, C. Rasmussen, S. Horton, Dominator colorings and safe clique partitions, Congressus numerantium 181 (2006) 19–23.
- R. Gera, On dominator colorings in graphs, Graph Theory Notes N. Y, LII(2007) 25–30.
- R. Gera, On the dominator colorings in bipartite graphs, Inf. Technol. New Gen. ITNG’07 (2007) 947–952.
- N. Ghanbari and S. Alikhani, More on the total dominator chromatic number of a graph, Journal of Information and Optimization Sciences 40(1) (2019) 157–169. doi: 10.1080/02522667.2018.1453665
- M.A. Henning, Total dominator colorings and total domination in graphs, Graphs and Combinatorics 31 (2015) 953–974. doi: 10.1007/s00373-014-1425-1
- C. Heuberger, On planarity and colorability of circulant graphs, Discrete Mathematics 268(1-3)(2003) 153–169. doi: 10.1016/S0012-365X(02)00685-4
- P. Jalilolghadr, A.P. Kazemi, A. Khodkar, Total Dominator coloring of circulant graphs Cn(a, b), (2019) ArXiv Preprint ArXiv:1905.00211.
- J.M. Jeyaseeli, M. Nazanin, S. Arumugam, Dominator coloring of generalized Petersen graphs, International conference on theoretical computer science and discrete mathematics (2016) 144–151.
- R. Kalaivani and D. Vijayalakshmi, On dominator coloring of degree splitting graph of some graphs, Journal of Physics: Conference Series 1139(1) 2018.
- R.M. Karp, Reducibility among combinatorial problems, in: R.E. Miller, J.W. Thatcher (Eds.), Complexity of computer computations, Plenum Press, New York, 1972, pp. 85–104.
- A.P. Kazemi, Total dominator chromatic number of a graph, (2013) arXiv preprint arXiv:1307.7486.
- A.P. Kazemi, Total dominator coloring in product graphs, Utilitas Mathematica 94 (2014) 329–345.
- S. Klavžar, Coloring graph products–a survey, Discrete Mathematics, 155(1-3) (1996) 135-145. doi: 10.1016/0012-365X(94)00377-U
- H.B. Merouane and M. Chellali, An algorithm for the dominator chromatic number of a tree, Journal of Combinatorial Optimization 30 (2015) 27–33. doi: 10.1007/s10878-013-9631-y
- B.S. Panda and P. Arti, On the dominator coloring in proper interval graphs and block graphs, Discrete Mathematics, Algorithms and Applications 7(4) (2015) 1550043 1–17. doi: 10.1142/S1793830915500433
- A.V. Rani and N. Parvathi, Chromatic number of some families of graphs, Journal of Discrete Mathematical Sciences and Cryptography, 22(6) (2019) 1141–1149. doi: 10.1080/09720529.2019.1689612