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The Subset-Strong Product of Graphs Cover
By: Mehdi Eliasi  
Open Access
|Jan 2024

References

  1. W.N. Anderson and T.D. Morley, Eigenvalues of the Laplacian of a graph, Linear and Multilinear Algebra 18 (1985), no. 2, 141–145.
  2. D. Archambault, T. Munzner, and D. Auber, TopoLayout: Multilevel graph layout by topological features, IEEE Trans. Vis. Comput. Graph. 13 (2007), no. 2, 305–317.
  3. D. Archambault, T. Munzner, and D. Auber, GrouseFlocks: Steerable exploration of graph hierarchy space, IEEE Trans. Vis. Comput. Graph. 14 (2008), no. 4, 900–913.
  4. M. Arezoomand and B. Taeri, Zagreb indices of the generalized hierarchical product of graphs, MATCH Commun. Math. Comput. Chem. 69 (2013), no. 1, 131–140.
  5. L. Barrière, C. Dalfó, M.A. Fiol, and M. Mitjana, The generalized hierarchical product of graphs, Discrete Math. 309 (2009), no. 12, 3871–3881.
  6. J. Braun, A. Kerber, M. Meringer, and C. Rücker, Similarity of molecular descriptors: the equivalence of Zagreb indices and walk counts, MATCH Commun. Math. Comput. Chem. 54 (2005), no. 1, 163–176.
  7. Q. Ding, W. Sun, and F. Chen, Applications of Laplacian spectra on a 3-prism graph, Modern Phys. Lett. B. 28 (2014), no. 2, 1450009, 12 pp.
  8. M. Eliasi and A. Iranmanesh, The hyper-Wiener index of the generalized hierarchical product of graphs, Discrete Appl. Math. 159 (2011), no. 8, 866–871.
  9. M. Eliasi, Gh. Raeisi, and B. Taeri, Wiener index of some graph operations, Discrete Appl. Math. 160 (2012), no. 9, 1333–1344.
  10. J. Feigenbaum and A.A. Schäffer, Finding the prime factors of strong direct product graphs in polynomial time, Discrete Math. 109 (1992), no. 1–3, 77–102.
  11. D.C. Fisher, J. Ryan, G. Domke, and A. Majumdar, Fractional domination of strong direct products, Discrete Appl. Math. 50 (1994), no. 1, 89–91.
  12. I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), no. 4, 535–538.
  13. R.S. Hales, Numerical invariants and the strong product of graphs, J. Combinatorial Theory Ser. B 15 (1973), 146–155.
  14. R. Hammack, W. Imrich, and S. Klavžar, Handbook of Product Graphs, CRC Press, Boca Raton, FL, 2011.
  15. Y.P. Hong, R.A. Horn, and C.R. Johnson, On the reduction of pairs of Hermitian or symmetric matrices to diagonal form by congruence, Linear Algebra Appl. 73 (1986), 213–226.
  16. A. Kaveh and H. Fazli, Approximate eigensolution of Laplacian matrices for locally modified graph products, J. Comput. Appl. Math. 236 (2011), no. 6, 1591–1603.
  17. A. Kaveh and K. Koohestani, Graph products for configuration processing of space structures, Comput. Struct. 86 (2008), no. 11–12, 1219–1231.
  18. A. Kaveh and R. Mirzaie, Minimal cycle basis of graph products for the force method of frame analysis, Comm. Numer. Methods Engrg. 24 (2008), no. 8, 653–669.
  19. M.H. Khalifeh, H. Yousefi-Azari, and A.R. Ashrafi, The hyper-Wiener index of graph operations, Comput. Math. Appl. 56 (2008), no. 5, 1402–1407.
  20. M.H. Khalifeh, H. Yousefi-Azari, and A.R. Ashrafi, The first and second Zagreb indices of some graph operations, Discrete Appl. Math. 157 (2009), no. 4, 804–811.
  21. S. Klavžar, Strong products of χ-critical graphs, Aequationes Math. 45 (1993), no. 2–3, 153–162.
  22. S. Klavžar and U. Milutinović, Strong products of Kneser graphs, Discrete Math. 133 (1994), no. 1–3, 297–300.
  23. J.-B. Liu, J. Cao, A. Alofi, A. AL-Mazrooei, and A. Elaiw, Applications of Laplacian spectra for n-prism networks, Neurocomputing 198 (2016), 69–73.
  24. Z. Luo, Applications on hyper-Zagreb index of generalized hierarchical product graphs, J. Comput. Theor. Nanosci. 13 (2016), no. 10, 7355–7361.
  25. S. Nikolić, G. Kovačević, A Miličević, and N. Trinajstić, The Zagreb indices 30 years after, Croat. Chem. Acta 76 (2003), no. 2, 113–124.
  26. K. Pattabiraman, S. Nagarajan, and M. Chendrasekharan, Zagreb indices and coindices of product graphs, J. Prime Res. Math. 10 (2014), 80–91.
  27. G. Sabidussi, Graph multiplication, Math. Z. 72 (1959), 446–457.
  28. S. Špacapan, Connectivity of strong products of graphs, Graphs Combin. 26 (2010), no. 3, 457–467.
  29. B. Zhou, Zagreb indices, MATCH Commun. Math. Comput. Chem. 52 (2004), 113–118.
  30. B. Zhou and I. Gutman, Relations between Wiener, hyper-Wiener and Zagreb indices, Chem. Phys. Lett. 394 (2004), no. 1–3, 93–95.
  31. B. Zhou and I. Gutman, Further properties of Zagreb indices, MATCH Commun. Math. Comput. Chem. 54 (2005), no. 1, 233–239.
DOI: https://doi.org/10.2478/amsil-2023-0029 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107
Language: English
Page range: 263 - 283
Submitted on: Apr 1, 2023
Accepted on: Dec 18, 2023
Published on: Jan 10, 2024
Published by: University of Silesia in Katowice, Institute of Mathematics
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2024 Mehdi Eliasi, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.