On the fault-tolerant metric dimension of certain interconnection networks
Tóm tắt
Từ khóa
Tài liệu tham khảo
Ahmad, A., Imran, M., Al-Mushayt, O., Bokhary, S.A.U.H.: On the metric dimension of barycentric subdividion of Cayley graph $$Cay(\mathbb{Z}_n\oplus \mathbb{Z}_m)$$ C a y ( Z n ⊕ Z m ) . Miskolc. Math. Notes 16(2), 637–646 (2015)
Bailey, R.F., Cameron, P.J.: Basie size, metric dimension and other invariants of groups and graphs. Bull. London Math. Soc. 43, 209–242 (2011)
Bailey, R.F., Meagher, K.: On the metric dimension of Grassmann graphs. Discrete Math. Theor. Comput. Sci. 13(4), 97–104 (2011)
Beerloiva, Z., Eberhard, F., Erlebach, T., Hall, A., Hoffmann, M., Mihalák, M., Ram, L.: Network discovery and verification. IEEE J. Sel. Area Commun. 24, 2168–2181 (2006)
Cáceres, J., Hernando, C., Mora, M., Pelayoe, I.M., Puertas, M.L.: On the metric dimension of infinite graphs. Electron. Notes Discrete Math. 35, 15–20 (2009)
Cáceres, J., Hernando, C., Mora, M., Pelayoe, I.M., Puertas, M.L., Seara, C., Wood, D.R.: On the metric dimension of cartesian products of graphs. SIAM J. Discrete Math. 21, 423–441 (2007)
Chartrand, G., Zhang, P.: The theory and applications of resolvability in graphs: A survey. In: Proceedings of the 34th Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congr. Numer. 160, 47–68 (2003)
Chartrand, G., Eroh, L., Johnson, M.A., Oellermann, O.R.: Resolvability in graphs and the metric dimension of a graph. Discrete Appl. Math. 150, 99–113 (2000)
Chen, M.S., Shin, K.G., Kandlur, D.D.: Addressing, routing and broadcasting in hexagonal mesh multiprocessors. IEEE Trans. Comput. 39, 10–18 (1990)
Fehr, M., Gosselin, S., Oellermann, O.: The metric dimension of Cayley digraphs. Discrete Math. 306, 31–41 (2006)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, New York (1979)
Harary, F., Melter, R.A.: On the metric dimension of a graph. Ars Combin. 2, 191–195 (1976)
Hayat, S.: Computing distance-based topological descriptors of complex chemical networks: new theoretical techniques. Chem. Phys. Lett. 688, 51–58 (2017)
Hayat, S., Malik, M.A., Imran, M.: Computing topological indices of honeycomb derived networks. Rom. J. Inf. Sci. Technol. 18, 144–165 (2015)
Hernando, C., Mora, M., Slater, P.J., Wood, D.R.: Fault-tolerant metric dimension of graphs. In: Proceedings of International Conference on Convexity in Discrete Structures, Ramanujan Mathematical Society Lecture Notes, pp. 81–85. May (2008)
Imran, M., Siddiqui, H.M.A.: Computing the metric dimension of convex polytopes generated by the wheel related graphs. Acta Math. Hung. 149, 10–30 (2016)
Javaid, I., Salman, M., Chaudhry, M.A., Shokat, S.: Fault-tolerance in resolvibility. Utilitas Math. 80, 263–275 (2009)
Khuller, S., Raghavachari, B., Rosenfeld, A.: Landmarks in graphs. Discrete Appl. Math. 70, 217–229 (1996)
Kratica, J., Kovačević-Vujčić, V., Čangalović, M., Stojanović, M.: Minimal doubly resolving sets and the strong metric dimension of some convex polytopes. Appl. Math. Comput. 218, 9790–9801 (2012)
Krishnan, S., Rajan, B.: Fault-tolerant resolvability of certain crystal structures. Appl. Math. 7, 599–604 (2016)
Liu, K., Abu-Ghazaleh, N.: Virtual coordinate back tracking for void travarsal in geographic routing. In: Kunz, T., Ravi, S.S. (eds.) Ad-Hoc, Mobile, and Wireless Networks. ADHOC-NOW 2006. Lecture Notes in Computer Science, vol. 4104. Springer, Berlin (2006)
Manuel, P., Rajan, B., Rajasingh, I., Monica, C.: On minimum metric dimension of honeycomb networks. J. Discrete Algorithms 6, 20–27 (2008)
Nocetti, F.G., Stojmenovic, I., Zhang, J.: Addressing and routing in hexagonal networks with applications for tracking mobile users and connection rerouting in cellular networks. IEEE Trans. Parallel Distrib. Syst. 13, 963–971 (2002)
Parhami, B., Kwai, D.-M.: A unified formulation of honeycomb and diamond networks. IEEE Trans. Parallel Distrib. Syst. 12, 74–79 (2001)
Raza, H., Hayat, S., Pan, X.-F.: On the fault-tolerant metric dimension of convex polytopes. Appl. Math. Comput. 339, 172–185 (2018)
Salman, M., Javaid, I., Chaudhry, M.A.: Minimum fault-tolerant, local and strong metric dimension of graphs, arXiv preprint arXiv:1409.2695 (2014), http://arxiv.org/pdf/1409.2695
Siddiqui, H.M.A., Imran, M.: Computing the metric dimension of wheel related graphs. Appl. Math. Comput. 242, 624–632 (2014)
Slater, P.J.: Leaves of trees. In: Proceedings of 6th Southeastern Conference on Combinatorics, Graph Theory, and Computing. Congr. Numer. 549–559 (1975)
Stojmenovic I.: Direct interconnection networks. In: Zomaya, A.Y. (ed.) Parallel and Distributed Computing Handbook, McGraw-Hill Professional, pp. 537–567 (1996)
Stojmenovic, I.: Honeycomb networks: topological properties and communication algorithms. IEEE Trans. Parallel Distrib. Syst. 8, 1036–1042 (1997)