대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제36권2호
  • /
  • Pages.389-400
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  • 2021
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  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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VARIABLE SUM EXDEG INDICES OF CACTUS GRAPHS

  • Du, Jianwei (School of Science North University of China) ;
  • Sun, Xiaoling (School of Science North University of China)
  • 투고 : 2019.07.03
  • 심사 : 2020.12.01
  • 발행 : 2021.04.30
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초록

For a graph G, the variable sum exdeg index SEIa(G) is defined as Σu∈V(G)dG(u)adG(u), where a ∈ (0, 1) ∪ (1, +∞). In this work, we determine the minimum and maximum variable sum exdeg indices (for a > 1) of n-vertex cactus graphs with k cycles or p pendant vertices. Furthermore, the corresponding extremal cactus graphs are characterized.

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과제정보

The authors would like to thank the referee for his/her careful reading and helpful suggestions.

참고문헌

  1. S. Akhter, M. Imran, and Z. Raza, On the general sum-connectivity index and general Randic index of cacti, J. Inequal. Appl. 2016 (2016), Paper No. 300, 9 pp. https://doi.org/10.1186/s13660-016-1250-6
  2. A. Ali and A. A. Bhatti, A note on the augmented Zagreb index of cacti with fixed number of vertices and cycles, Kuwait J. Sci. 43 (2016), no. 4, 11-17.
  3. A. Ali, A. A. Bhatti, and Z. Raza, A note on the zeroth-order general Randic index of cacti and polyomino chains, Iranian J. Math. Chem. 5 (2014), 143-152.
  4. A. R. Ashrafi, T. Dehghan-Zadeh, and N. Habibi, Extremal atom-bond connectivity index of cactus graphs, Commun. Korean Math. Soc. 30 (2015), no. 3, 283-295. https://doi.org/10.4134/CKMS.2015.30.3.283
  5. J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, Elsvier, New York, 1976.
  6. H. Dong and X. Wu, On the atom-bond connectivity index of cacti, Filomat 28 (2014), no. 8, 1711-1717. https://doi.org/10.2298/FIL1408711D
  7. A. Ghalavand and A. R. Ashrafi, Extremal graphs with respect to variable sum exdeg index via majorization, Appl. Math. Comput. 303 (2017), 19-23. https://doi.org/10.1016/j.amc.2017.01.007
  8. I. Gutman and B. Furtula (Eds.), Novel Molecular Structure Descriptors - Theory and Applications I, Univ. Kragujevac, Kragujevac, 2010.
  9. I. Gutman and B. Furtula (Eds.), Novel Molecular Structure Descriptors - Theory and Applications II, Univ. Kragujevac, Kragujevac, 2010.
  10. I. Gutman, S. Li, and W. Wei, Cacti with n-vertices and t cycles having extremal Wiener index, Discrete Appl. Math. 232 (2017), 189-200. https://doi.org/10.1016/j.dam.2017.07.023
  11. S. Li, H. Yang, and Q. Zhao, Sharp bounds on Zagreb indices of cacti with k pendant vertices, Filomat 26 (2012), no. 6, 1189-1200. https://doi.org/10.2298/FIL1206189L
  12. L. Lin and M. Lu, On the zeroth-order general Randic index of cacti, Ars Combin. 106 (2012), 381-393.
  13. A. Lin, R. Luo, and X. Zha, A sharp lower bound of the Randic index of cacti with r pendants, Discrete Appl. Math. 156 (2008), no. 10, 1725-1735. https://doi.org/10.1016/j.dam.2007.08.031
  14. H. Liu and M. Lu, A unified approach to extremal cacti for different indices, MATCH Commun. Math. Comput. Chem. 58 (2007), no. 1, 183-194.
  15. M. Lu, L. Zhang, and F. Tian, On the Randic index of cacti, MATCH Commun. Math. Comput. Chem. 56 (2006), no. 3, 551-556.
  16. F. Ma and H. Deng, On the sum-connectivity index of cacti, Math. Comput. Modelling 54 (2011), no. 1-2, 497-507. https://doi.org/10.1016/j.mcm.2011.02.040
  17. R. Todeschini and V. Consonni, Handbook of Molecular Descriptors, Wiley-VCH, Weinheim, 2000.
  18. D. Vukicevic, Bond additive modeling. adriatic indices overview of the results, in I. Gutman and B. Furtula (Eds.), Novel Molecular Structure Descriptors. Theory and Applications II, 269-302, Univ. Kragujevac, Kragujevac, 2010.
  19. D. Vukicevic, Bond additive modeling 3. QSPR and QSAR studies of the variable Adriatic indices, Croat. Chem. Acta 83 (2010), 349-351.
  20. D. Vukicevic, Bond additive modeling 4. QSPR and QSAR studies of the variable Adriatic indices, Croat. Chem. Acta 84 (2011), 87-91. https://doi.org/10.5562/cca1666
  21. D. Vukicevic, Bond additive modeling 5. mathematical properties of the variable sum exdeg index, Croat. Chem. Acta 84 (2011), 93-101. https://doi.org/10.5562/cca1667
  22. D. Vukicevic, Bond additive modeling 6. Randomness vs. design, MATCH Commun. Math. Comput. Chem. 65 (2011), no. 2, 415-426.
  23. S. Wang, On extremal cacti with respect to the Szeged index, Appl. Math. Comput. 309 (2017), 85-92. https://doi.org/10.1016/j.amc.2017.03.036
  24. H. Wang and L. Kang, On the Harary index of cacti, Util. Math. 96 (2015), 149-163.
  25. D. Wang and S. Tan, The maximum hyper-Wiener index of cacti, J. Appl. Math. Comput. 47 (2015), no. 1-2, 91-102. https://doi.org/10.1007/s12190-014-0763-8
  26. Z. Yarahmadi and A. R. Ashrafi, The exdeg polynomial of some graph operations and applications in nanoscience, J. Comput. Theor. Nanosci. 12 (2015), 45-51.