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Year 2021, , 132 - 135, 30.12.2021
https://doi.org/10.32323/ujma.973671

Abstract

References

  • [1] B. Bollob´as, Extremal Graph Theory, Academic Press, London (1978), Pages 295 and 296.
  • [2] J.A. Bondy, U.S.R. Murty, Graph Theory with Applications, Macmillan, London and Elsevier, New York (1976).
  • [3] B. Borovi´canin, K. Das, B. Furtula, I. Gutman, Bounds for Zagreb indices, MATCH Commun. Math. Comput. Chem. 78 (2017), 17–100.
  • [4] Y. Caro, New results on the independence number, Technical Report, Tel-Aviv University, 1979.
  • [5] C. S. Edwards and C. H. Elphick, Lower bounds for the clique and the chromatic numbers of a graph, Discrete Appl. Math., 5 (1983,) 51–64.
  • [6] P. Erd˝os, On the graph theorem of Tur´an (in Hungarian), Mat. Lapok, 21 (1970), 249–251.
  • [7] S. Filipovski, New bounds for the first Zagreb index, MATCH Commun Math Comput Chem., 54 (2005), 195–208.
  • [8] I. Gutman and N. Trinajsti´c, Graph theory and molecular orbitals, total p–electron energy of alternant hydroncarbons, Chem. Phys. Lett., 17 (1972), 535–538.
  • [9] X. Li and Z. Zheng, A unified approach to the extremal trees for different indices, MATCH Commun. Math. Comput. Chem,. 85(2021), 303–312.
  • [10] V. K. Wei, A lower bound on the stability number of a simple graph, Bell Laboratories Technical Memorandum, No. 81-11217-9, 1981.

The Bounds for the First General Zagreb Index of a Graph

Year 2021, , 132 - 135, 30.12.2021
https://doi.org/10.32323/ujma.973671

Abstract

The first general Zagreb index of a graph $G$ is defined as the sum of the $\alpha$th powers of the vertex degrees of $G$, where $\alpha$ is a real number such that $\alpha \neq 0$ and $\alpha \neq 1$. In this note, for $\alpha > 1$, we present upper bounds involving chromatic and clique numbers for the first general Zagreb index of a graph; for an integer $\alpha \geq 2$, we present a lower bound involving the independence number for the first general Zagreb index of a graph.

References

  • [1] B. Bollob´as, Extremal Graph Theory, Academic Press, London (1978), Pages 295 and 296.
  • [2] J.A. Bondy, U.S.R. Murty, Graph Theory with Applications, Macmillan, London and Elsevier, New York (1976).
  • [3] B. Borovi´canin, K. Das, B. Furtula, I. Gutman, Bounds for Zagreb indices, MATCH Commun. Math. Comput. Chem. 78 (2017), 17–100.
  • [4] Y. Caro, New results on the independence number, Technical Report, Tel-Aviv University, 1979.
  • [5] C. S. Edwards and C. H. Elphick, Lower bounds for the clique and the chromatic numbers of a graph, Discrete Appl. Math., 5 (1983,) 51–64.
  • [6] P. Erd˝os, On the graph theorem of Tur´an (in Hungarian), Mat. Lapok, 21 (1970), 249–251.
  • [7] S. Filipovski, New bounds for the first Zagreb index, MATCH Commun Math Comput Chem., 54 (2005), 195–208.
  • [8] I. Gutman and N. Trinajsti´c, Graph theory and molecular orbitals, total p–electron energy of alternant hydroncarbons, Chem. Phys. Lett., 17 (1972), 535–538.
  • [9] X. Li and Z. Zheng, A unified approach to the extremal trees for different indices, MATCH Commun. Math. Comput. Chem,. 85(2021), 303–312.
  • [10] V. K. Wei, A lower bound on the stability number of a simple graph, Bell Laboratories Technical Memorandum, No. 81-11217-9, 1981.
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Rao Li

Publication Date December 30, 2021
Submission Date July 21, 2021
Acceptance Date November 22, 2021
Published in Issue Year 2021

Cite

APA Li, R. (2021). The Bounds for the First General Zagreb Index of a Graph. Universal Journal of Mathematics and Applications, 4(4), 132-135. https://doi.org/10.32323/ujma.973671
AMA Li R. The Bounds for the First General Zagreb Index of a Graph. Univ. J. Math. Appl. December 2021;4(4):132-135. doi:10.32323/ujma.973671
Chicago Li, Rao. “The Bounds for the First General Zagreb Index of a Graph”. Universal Journal of Mathematics and Applications 4, no. 4 (December 2021): 132-35. https://doi.org/10.32323/ujma.973671.
EndNote Li R (December 1, 2021) The Bounds for the First General Zagreb Index of a Graph. Universal Journal of Mathematics and Applications 4 4 132–135.
IEEE R. Li, “The Bounds for the First General Zagreb Index of a Graph”, Univ. J. Math. Appl., vol. 4, no. 4, pp. 132–135, 2021, doi: 10.32323/ujma.973671.
ISNAD Li, Rao. “The Bounds for the First General Zagreb Index of a Graph”. Universal Journal of Mathematics and Applications 4/4 (December 2021), 132-135. https://doi.org/10.32323/ujma.973671.
JAMA Li R. The Bounds for the First General Zagreb Index of a Graph. Univ. J. Math. Appl. 2021;4:132–135.
MLA Li, Rao. “The Bounds for the First General Zagreb Index of a Graph”. Universal Journal of Mathematics and Applications, vol. 4, no. 4, 2021, pp. 132-5, doi:10.32323/ujma.973671.
Vancouver Li R. The Bounds for the First General Zagreb Index of a Graph. Univ. J. Math. Appl. 2021;4(4):132-5.

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