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Year 2021, , 251 - 257, 01.12.2021
https://doi.org/10.33401/fujma.975352

Abstract

References

  • [1] Y. Alavi, M. Behzad, P. Erdos, D. R. Lick, Double vertex graphs, J. Comb. Inf. Syst. Sci., 16(1) (1991), 37-50.
  • [2] Y. Alavi, M. Behzad, J. E. Simpson, Planarity of Double Vertex Graphs, Graph theory, combinatorics, algorithms, and applications (San Francisco, CA) (1991), 472-485.
  • [3] Y. Alavi, D. R. Lick, J. Liu, Survey of double vertex graphs, Graphs Combin., 18(4) (2002), 709-715.
  • [4] T. Rudolph, Constructing physically intuitive graph invariants, (2002), arXiv:quant-ph/0206068.
  • [5] K. Audenaert, C. Godsil, G. Royle, T. Rudolph, Symmetric squares of graphs, J. Combin. Theory Ser. B, 97(1) (2007), 74-90.
  • [6] R. Fabila-Monroy, D. Flores-Pe˜naloza, C. Huemer, F. Hurtado, J. Urrutia, D. R. Wood, Token graphs, Graphs Combin., 28(3) (2012), 365-380.
  • [7] L. Adame, L. M. Rivera, A. L. Trujillo-Negrete, Hamiltonicity of the double vertex graph and the complete double vertex graph of some join graphs, (2020), arXiv:2007.00115 [math.CO].
  • [8] L. Adame, L. M. Rivera, A. L. Trujillo-Negrete, Hamiltonicity of token graphs of some join graphs, Symmetry, 13(6) (2021), 1076.
  • [9] H. de Alba, W. Carballosa, J. Lea˜nos, L. M. Rivera, Independence and matching numbers of some token graphs, Australas. J. Combin., 76 (2020), 387-403.
  • [10] J. Deepalakshmi, G. Marimuthu, Characterization of token graphs, J. Eng. Technol., 6 (2017), 310-317.
  • [11] J. Deepalakshmi, G. Marimuthu, A. Somasundaram, S. Arumugam, On the 2-token graph of a graph, AKCE Int. J. Graphs Comb., 17(1) (2019), 265-268.
  • [12] P. Jimenez-Sep´ulveda, L. M. Rivera, Independence numbers of some double vertex graphs and pair graphs, (2018), arXiv:1810.06354 [math.CO].
  • [13] S. S. Kumar, R. Sundareswaran, M. Sundarakannan, On Zagreb indices of double vertex graphs, TWMS J. Appl. Eng. Math., 10(4) (2020), 1096-1104.
  • [14] J. G. Soto, J. Lea˜nos, L. M. R´ıos-Castro, L. M. Rivera, The packing number of the double vertex graph of the path graph, Discrete Appl. Math., 247 (2018), 327-340.
  • [15] F. Harary, Conditional connectivity, Networks, 13(3) (1983), 347-357.
  • [16] F. Boesch, R. Tindell, Circulants and their connectivities, J. Graph Theory, 8(4) (1984), 487-499.
  • [17] W. Yang, J. Meng, Extraconnectivity of hypercubes, Appl. Math. Lett., 22(6) (2009), 887-891.
  • [18] W. Yang, J. Meng, Extraconnectivity of hypercubes (II), Australas. J. Comb., 47 (2010), 189-196.
  • [19] G. B. Ekinci, A. Kırlangic¸, Super connectivity of Kronecker product of complete bipartite graphs and complete graphs, Discrete Math., 339(7) (2016), 1950-1953.
  • [20] L. Guo, C. Qin, X. Guo, Super connectivity of Kronecker products of graphs, Inform. Process. Lett., 110 (16) (2010), 659-661.
  • [21] M. L¨u, C. Wu, G.-L. Chen, C. Lv, On super connectivity of Cartesian product graphs, Networks, 52(2) (2008), 78-87.
  • [22] J. Lea˜nos, A. L. Trujillo-Negrete, The connectivity of token graphs, Graphs Combin., 34(4) (2018), 777-790.
  • [23] J. Lea˜nos, C. Ndjatchi, The edge-connectivity of token graphs, Graphs Combin., 37(3) (2021), 1013-1023.
  • [24] R. Fabila-Monroy, J. Lea˜nos, A. L. Trujillo-Negrete, On the connectivity of token graphs of trees, (2020), arXiv:2004.14526 [math.CO].
  • [25] G. B. Ekinci, J. B. Gauci, The super-connectivity of Johnson graphs, Discrete Math. Theor. Comput. Sci., 22(1) (2020).

The Super-Connectivity of the Double Vertex Graph of Complete Bipartite Graphs

Year 2021, , 251 - 257, 01.12.2021
https://doi.org/10.33401/fujma.975352

Abstract

Let $ G=(V,E) $ be a graph. The double vertex graph $F_2(G)$ of $ G $ is the graph whose vertex set consists of all $ 2 $-subsets of $ V(G) $ such that two vertices are adjacent in $ F_2(G) $ if their symmetric difference is a pair of adjacent vertices in $ G $. The super--connectivity of a connected graph is the minimum number of vertices whose removal results in a disconnected graph without an isolated vertex. In this paper, we determine the super--connectivity of the double vertex graph of the complete bipartite graph $ K_{m,n} $ for $ m\geq 4 $ where $ n\geq m+2 $.

References

  • [1] Y. Alavi, M. Behzad, P. Erdos, D. R. Lick, Double vertex graphs, J. Comb. Inf. Syst. Sci., 16(1) (1991), 37-50.
  • [2] Y. Alavi, M. Behzad, J. E. Simpson, Planarity of Double Vertex Graphs, Graph theory, combinatorics, algorithms, and applications (San Francisco, CA) (1991), 472-485.
  • [3] Y. Alavi, D. R. Lick, J. Liu, Survey of double vertex graphs, Graphs Combin., 18(4) (2002), 709-715.
  • [4] T. Rudolph, Constructing physically intuitive graph invariants, (2002), arXiv:quant-ph/0206068.
  • [5] K. Audenaert, C. Godsil, G. Royle, T. Rudolph, Symmetric squares of graphs, J. Combin. Theory Ser. B, 97(1) (2007), 74-90.
  • [6] R. Fabila-Monroy, D. Flores-Pe˜naloza, C. Huemer, F. Hurtado, J. Urrutia, D. R. Wood, Token graphs, Graphs Combin., 28(3) (2012), 365-380.
  • [7] L. Adame, L. M. Rivera, A. L. Trujillo-Negrete, Hamiltonicity of the double vertex graph and the complete double vertex graph of some join graphs, (2020), arXiv:2007.00115 [math.CO].
  • [8] L. Adame, L. M. Rivera, A. L. Trujillo-Negrete, Hamiltonicity of token graphs of some join graphs, Symmetry, 13(6) (2021), 1076.
  • [9] H. de Alba, W. Carballosa, J. Lea˜nos, L. M. Rivera, Independence and matching numbers of some token graphs, Australas. J. Combin., 76 (2020), 387-403.
  • [10] J. Deepalakshmi, G. Marimuthu, Characterization of token graphs, J. Eng. Technol., 6 (2017), 310-317.
  • [11] J. Deepalakshmi, G. Marimuthu, A. Somasundaram, S. Arumugam, On the 2-token graph of a graph, AKCE Int. J. Graphs Comb., 17(1) (2019), 265-268.
  • [12] P. Jimenez-Sep´ulveda, L. M. Rivera, Independence numbers of some double vertex graphs and pair graphs, (2018), arXiv:1810.06354 [math.CO].
  • [13] S. S. Kumar, R. Sundareswaran, M. Sundarakannan, On Zagreb indices of double vertex graphs, TWMS J. Appl. Eng. Math., 10(4) (2020), 1096-1104.
  • [14] J. G. Soto, J. Lea˜nos, L. M. R´ıos-Castro, L. M. Rivera, The packing number of the double vertex graph of the path graph, Discrete Appl. Math., 247 (2018), 327-340.
  • [15] F. Harary, Conditional connectivity, Networks, 13(3) (1983), 347-357.
  • [16] F. Boesch, R. Tindell, Circulants and their connectivities, J. Graph Theory, 8(4) (1984), 487-499.
  • [17] W. Yang, J. Meng, Extraconnectivity of hypercubes, Appl. Math. Lett., 22(6) (2009), 887-891.
  • [18] W. Yang, J. Meng, Extraconnectivity of hypercubes (II), Australas. J. Comb., 47 (2010), 189-196.
  • [19] G. B. Ekinci, A. Kırlangic¸, Super connectivity of Kronecker product of complete bipartite graphs and complete graphs, Discrete Math., 339(7) (2016), 1950-1953.
  • [20] L. Guo, C. Qin, X. Guo, Super connectivity of Kronecker products of graphs, Inform. Process. Lett., 110 (16) (2010), 659-661.
  • [21] M. L¨u, C. Wu, G.-L. Chen, C. Lv, On super connectivity of Cartesian product graphs, Networks, 52(2) (2008), 78-87.
  • [22] J. Lea˜nos, A. L. Trujillo-Negrete, The connectivity of token graphs, Graphs Combin., 34(4) (2018), 777-790.
  • [23] J. Lea˜nos, C. Ndjatchi, The edge-connectivity of token graphs, Graphs Combin., 37(3) (2021), 1013-1023.
  • [24] R. Fabila-Monroy, J. Lea˜nos, A. L. Trujillo-Negrete, On the connectivity of token graphs of trees, (2020), arXiv:2004.14526 [math.CO].
  • [25] G. B. Ekinci, J. B. Gauci, The super-connectivity of Johnson graphs, Discrete Math. Theor. Comput. Sci., 22(1) (2020).
There are 25 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Gülnaz Boruzanlı Ekinci 0000-0002-6733-6321

Publication Date December 1, 2021
Submission Date July 28, 2021
Acceptance Date October 26, 2021
Published in Issue Year 2021

Cite

APA Boruzanlı Ekinci, G. (2021). The Super-Connectivity of the Double Vertex Graph of Complete Bipartite Graphs. Fundamental Journal of Mathematics and Applications, 4(4), 251-257. https://doi.org/10.33401/fujma.975352
AMA Boruzanlı Ekinci G. The Super-Connectivity of the Double Vertex Graph of Complete Bipartite Graphs. Fundam. J. Math. Appl. December 2021;4(4):251-257. doi:10.33401/fujma.975352
Chicago Boruzanlı Ekinci, Gülnaz. “The Super-Connectivity of the Double Vertex Graph of Complete Bipartite Graphs”. Fundamental Journal of Mathematics and Applications 4, no. 4 (December 2021): 251-57. https://doi.org/10.33401/fujma.975352.
EndNote Boruzanlı Ekinci G (December 1, 2021) The Super-Connectivity of the Double Vertex Graph of Complete Bipartite Graphs. Fundamental Journal of Mathematics and Applications 4 4 251–257.
IEEE G. Boruzanlı Ekinci, “The Super-Connectivity of the Double Vertex Graph of Complete Bipartite Graphs”, Fundam. J. Math. Appl., vol. 4, no. 4, pp. 251–257, 2021, doi: 10.33401/fujma.975352.
ISNAD Boruzanlı Ekinci, Gülnaz. “The Super-Connectivity of the Double Vertex Graph of Complete Bipartite Graphs”. Fundamental Journal of Mathematics and Applications 4/4 (December 2021), 251-257. https://doi.org/10.33401/fujma.975352.
JAMA Boruzanlı Ekinci G. The Super-Connectivity of the Double Vertex Graph of Complete Bipartite Graphs. Fundam. J. Math. Appl. 2021;4:251–257.
MLA Boruzanlı Ekinci, Gülnaz. “The Super-Connectivity of the Double Vertex Graph of Complete Bipartite Graphs”. Fundamental Journal of Mathematics and Applications, vol. 4, no. 4, 2021, pp. 251-7, doi:10.33401/fujma.975352.
Vancouver Boruzanlı Ekinci G. The Super-Connectivity of the Double Vertex Graph of Complete Bipartite Graphs. Fundam. J. Math. Appl. 2021;4(4):251-7.

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