Search Results

1 - 10 of 65 items :

  • Cartesian product x
  • Discrete Mathematics x
Clear All
On Path-Pairability in the Cartesian Product of Graphs

References [1] W. Imrich and S. Klavžar, Product Graphs: Structure and Recognition (J. Wiley & Sons, New York, 2000). [2] W.-S. Chiue and B.-S. Shieh, On connectivity of the Cartesian product of two graphs, Appl. Math. Comput. 102 (1999) 129-137. doi:10.1016/S0096-3003(98)10041-3 [3] L. Csaba, R.J. Faudree, A. Gyárfás, J. Lehel and R.H. Schelp, Networks communi- cating for each pairing of terminals, Networks 22 (1992) 615-626. doi:10.1002/net.3230220702 [4] R.J. Faudree, Properties in pairable

Open access
Edge-Transitive Lexicographic and Cartesian Products

York, 2001). doi: 10.1007/978-1-4613-0163-9 [5] T. Gologranc, G. Mekiš and I. Peterin, Rainbow connection and graph products, Graphs Combin. 30 (2014) 591-607. doi: 10.1007/s00373-013-1295-y [6] R. Hammack, W. Imrich and S. Klavžar, Handbook of Product Graphs (Second Edition, CRC Press, Boca Raton, FL, 2011). [7] W. Imrich, Automorphismen und das kartesische Produkt von Graphen, Österreich. Akad. Wiss. Math.-Natur. Kl. S.-B. II 177 (1969) 203-214. [8] W. Imrich, Embedding graphs into Cartesian products

Open access
On the Crossing Numbers of Cartesian Products of Wheels and Trees

References [1] D. Archdeacon and R.B. Richter, On the parity of crossing numbers, J. Graph Theory 12 (1988) 307-310. doi: 10.1002/jgt.3190120302 [2] K. Asano, The crossing number of K1,3,n and K2,3,n, J. Graph Theory 10 (1986) 1-8. doi: 10.1002/jgt.3190100102 [3] L.W. Beineke and R.D. Ringeisen, On the crossing numbers of products of cycles and graphs of order four , J. Graph Theory 4 (1980) 145-155. doi: 10.1002/jgt.3190040203 [4] D. Bokal, On the crossing numbers of Cartesian products with

Open access
Distinguishing Cartesian Products of Countable Graphs

R eferences [1] M.O. Albertson, Distinguishing Cartesian powers of graphs , Electron. J. Combin. 12 (2005) #N17. [2] M.O. Albertson and K.L. Collins, Symmetry breaking in graphs , Electron. J. Combin. 3 (1996) #R18. [3] R. Hammack, W. Imrich and S. Klavžar, Handbook of Product Graphs (Second Edition), (Taylor & Francis Group, 2011). [4] W. Imrich, Automorphismen und das kartesische Produkt von Graphen , Österreich. Akad. Wiss. Math.-Natur. Kl. S.-B. II 177 (1969) 203–214. [5] W. Imrich, Über das schwache kartesische Produkt

Open access
On the Crossing Numbers of Cartesian Products of Stars and Graphs of Order Six

References 1] K. Asano, The crossing number of K1,3,n and K2,3,n, J. Graph Theory 10 (1986) 1-8. doi:10.1002/jgt.3190100102 [2] L.W. Beineke and R.D. Ringeisen, On the crossing numbers of products of cycles and graphs of order four , J. Graph Theory 4 (1980) 145-155. doi:10.1002/jgt.3190040203 [3] D. Bokal, On the crossing number of Cartesian products with paths, J. Combin. Theory (B) 97 (2007) 381-384. doi:10.1016/j.jctb.2006.06.003 [4] D. Bokal, On the crossing numbers of Cartesian

Open access
On Total Domination in the Cartesian Product of Graphs

R eferences [1] B. Brešar, P. Dorbec, W. Goddard, B.L. Hartnell, M.A. Henning, S. Klavžar and D.F. Rall, Vizing’s conjecture: a survey and recent results , J. Graph Theory 69 (2012) 46–76. doi:10.1002/jgt.20565 [2] B. Brešar, M.A. Henning and D.F. Rall, Paired-domination of Cartesian products of graphs and rainbow domination , Electron. Notes Discrete Math. 22 (2005) 233–237. doi:10.1016/j.endm.2005.06.059 [3] R.C. Brigham, J.R. Carrington and R.P. Vitray, Connected graphs with maximum total domination number , J. Combin. Math. Combin

Open access
On the Domination of Cartesian Product of Directed Cycles: Results for Certain Equivalence Classes of Lengths

References [1] T.Y. Chang and W.E. Clark, The domination numbers of the 5 × n and 6 × n grid graphs, J. Graph Theory 17 (1993) 81-107. doi:10.1002/jgt.3190170110 [2] M. El-Zahar and C.M. Pareek, Domination number of products of graphs, Ars Combin. 31 (1991) 223-227. [3] M. El-Zahar, S. Khamis and Kh. Nazzal, On the domination number of the Cartesian product of the cycle of length n and any graph, Discrete Appl. Math. 155 (2007) 515-522. doi:10.1016/j.dam.2006.07.003 [4] R.J. Faudree and R

Open access
Arc Fault Tolerance of Cartesian Product of Regular Digraphs on Super-Restricted Arc-Connectivity

] C.W. Cheng and S.Y. Hsieh, Bounds for the super extra edge connectivity of graphs, in: International Computing and Combinatorics Conference, D. Xu, D. Du, D. Du (Ed(s)), Lecture Notes in Comput. Sci. 9198 (2015) 624-631. doi: 10.1007/978-3-319-21398-9 49 [5] X. Chen, J. Liu and J. Meng, The restricted arc connectivity of Cartesian product digraphs, Inform. Process. Lett. 109 (2009) 1202-1205. doi: 10.1016/j.ipl.2009.08.005 [6] A.H. Esfahanian and S.L. Hakimi, On computing a conditional edge-connectivity of a graph, Inform. Process

Open access
Motion planning in cartesian product graphs

References [1] G. Calinescu, A. Dumitrescu and J. Pach, Reconfigurations in graphs and grids, in: Latin American Theoretical Informatics Conference Lecture Notes in Computer Science 3887 (2006) 262-273. doi:10.1007/11682462 27 [2] B. Deb, K. Kapoor and S. Pati, On mrj reachability in trees Discrete Math., Alg. and Appl. 4 (2012). doi:10.1142/S1793830912500553 [3] T. Feder, Stable Networks and Product Graphs (Memoirs of the American Mathe- matical Society, 1995). doi:10.1090/memo/0555 [4] R

Open access
The Thickness of Amalgamations and Cartesian Product of Graphs

, On topological invariants of the product of graphs , Canad. Math. Bull. 12 (1969) 157–166. doi:10.4153/CMB-1969-015-9 [9] J.A. Bondy and U.S.R.Murty, Graph Theory (Springer, 2008). [10] J.E. Chen, S.P. Kanchi and A. Kanevsky, A note on approximating graph genus , Inform. Process Lett. 61 (1997) 317–322. doi:10.1016/S0020-0190(97)00203-2 [11] R.J. Cimikowski, On heuristics for determining the thickness of a graph , Inform. Sci. 85 (1995) 87–98. doi:10.1016/0020-0255(95)00011-D [12] A.M. Dean, J.P. Hutchinson and E.R. Scheinerman, On

Open access