. (2010b). Measures to represent the properties of nodes in a directed graph, Information 13(3): 537-549. Lancaster, P. and Tismenetsky, M. (1985). The Theory of Matrices, Academic Press, New York, NY. Ligęza, A. and Ko´scielny, J.M. (2008). A new approach to multiple fault diagnosis: A combination of diagnostic matrices, graphs, algebraic and rule-based models. The case of two-layer models, International Journal of Applied Mathematics and Computer Science 18(4): 465-476, DOI: 10.2478/v10006-008-0041-8. Nilson, L. (2007

### Sándor Szabó and Bogdán Zaválnij

References [1] I. M. Bomze, M. Budinich, P. M. Pardalos, M. Pelillo, The maximum clique problem, in Handbook of Combinatorial Optimization Vol. 4, Eds. D.-Z. Du and P. M. Pardalos, Kluwer Academic Publisher, Boston, MA 1999. ⇒118 [2] R. Carraghan, P. M. Pardalos, An exact algorithm for the maximum clique problem, Operation Research Letters 9, 6 (1990), 375-382. ⇒118 [3] P. Erdős, L. Moser, On the representation of directed graphs as unions of orderings. Magyar Tud. Akad. Mat. Kutató Int. Közl. 9 (1964), 125

### Vitaly Zabiniako and Pavel Rusakov

- 10, 2009, J. Grundspenkis, M. Kirikova, Y. Manolopoulos, L. Novickis, Eds. Berlin: Springer- Verlag Berlin Heidelberg, 2010. pp. 193-201. [5] V. Zabiniako and P. Rusakov, “Supporting Visual Techniques for Graphs Data Analysis in Three-Dimensional Space” in Research Communications: 17th International Conference on Information and Software Technologies, IT 2011, Kaunas, Lithuania, April 27 - 29, 2011, R. Butleris, R. Butkiene, Eds. Kaunas: Kaunas University of Technology, 2011. pp. 75-87. [6] C. C. Lin and H. C. Yen, “A new force-directed

### Nasrin Dehgardi and Maryam Atapour

References [1] M. Atapour, A. Bodaghli and S.M. Sheikholeslami, Twin signed total domination numbers in directed graphs, Ars Combin., to appear. [2] M. Atapour and A. Khodkar, Twin minus domination numbers in directed graphs, Commun. Comb. Optim. 1 (2016) 149-164. doi: 10.22049/CCO.2016.13575 [3] M. Atapour, S. Norouzian, S.M. Sheikholeslami and L. Volkmann, Twin signed domination numbers in directed graphs, Algebra Discrete Math., to appear. [4] A. Bodaghli, S.M. Sheikholeslami and L. Volkmann

### Fan Yang, Sirish Shah and Deyun Xiao

(8): 1137-1152. Mosterman, P. J. and Biswas, G. (1999). Diagnosis of continuous valued systems in transient operating regions, IEEE Transactions on Systems, Man, and Cybernetics: Part A 29 (6): 554-565. Oyeleye, O. O. and Kramer, M. A. (1988). Qualitative simulation of chemical process systems: Steady-state analysis, AIChE Journal 34 (9): 1441-1454. Palmer, C. and Chung, P. W. H. (1999). Verifying signed directed graph models for process plants, Computers & Chemical Engineering

### Hong-Hai Li, Li Su and Jing Zhang

, On the addressing problem for loop switching, Bell. System Tech. J. 50 (1971) 2495-2519. [5] R.L. Graham, A.J. Hoffman and H. Hosoya, On the distance matrix of a directed graph, J. Graph Theory 1 (1977) 85-88. doi:10.1002/jgt.3190010116 [6] S.G. Guo, The spectral radius of unicyclic and bicyclic graphs with n vertices and k pendant vertices, Linear Algebra Appl. 408 (2005) 78-85. doi:10.1016/j.laa.2005.05.022 [7] S. Sivasubramanian, A q-analogue of Graham, Hoffman and Hosoya’s result , Electron. J. Combin. 17 (2010

### Simon Špacapan

independent sets in direct products of some vertex-transitive graphs , Acta Math. Sin. (Engl. Ser.) 28 (2012) 697–706. doi:10.1007/s10114-011-0311-5 [5] R. Hammack, W. Imrich and S. Klavžar, Handbook of Product Graphs, Second Edition (CRC Press, Boca Raton, FL, 2011). [6] S.T. Hedetniemi, Homomorphisms and graph automata, University of Michigan Technical Report 03105–44–T (1966). [7] P.K. Jha and S. Klavžar, Independence in direct-product graphs , Ars Combin. 50 (1998) 53–63. [8] B. Larose and C. Tardif, Projectivity and independent sets in

### Dániel A. Drexler and Péter Arató

.,”Decomposition of Graphs into Paths and Cycles”, Journal of Discrete Mathematics, Hindawi Publishing Corporation, pp. 1.6, 2013. [5] Kernighan, B. and Lin, S.,” An efficient heuristic procedure for partitioning graphs”, Bell System Technical Journal, 29l, pp. 291-307, 1970. [6] Hendrickson, B., and Leland, R., “Multidimensional Spectral Load Balancing, SAND93-0074”, Sandia National Laboratories, Albuquerque, NM, USA, 1993. [7] Leland, R., and Hendrickson, B., “An empirical study of static load balancing algorithms”, in Proceedings

### Tjaša Paj and Simon Špacapan

) 105-110. doi:10.1016/j.disc.2012.09.008 [4] L.M. Friedler, The independence number of the Cartesian product of graphs, Ars Combin. 99 (2011) 205-216. [5] D. Greenwell and L. Lovász, Applications of product colouring, Acta Math. Acad. Sci. Hungar. 25 (1974) 335-340. doi:/10.1007/BF01886093 [6] X.B. Geng, J. Wang and H. Zhang, Structure of independent sets in direct products of some vertex-transitive graphs, Acta Math. Sin. (Engl. Ser.) 28 (2012) 697-706. [7] J. Hagauer and S. Klavžar, On independence

### Michel Mollard

). [8] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs: Advanced Topics (Marcel Dekker, Inc. New York, 1998). [9] M.S. Jacobson and L.F. Kinch, On the domination number of products of graphs I , Ars Combin. 18 (1983) 33-44. [10] S. Klavžar and N. Seifter, Dominating Cartesian products of cycles, Discrete Appl. Math. 59 (1995) 129-136. doi:10.1016/0166-218X(93)E0167-W [11] J. Liu, X.D. Zhang, X. Chenand and J. Meng, On domination number of Cartesian product of directed cycles, Inform. Process. Lett. 110