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Some Bounds on Zeroth-Order General Randić Index

Author

Listed:
  • Muhammad Kamran Jamil

    (Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, P. O. Box 54600, Lahore, Pakistan
    Department of Mathematical Sciences, United Arab Emirates University, P. O. Box 15551, Al Ain, UAE)

  • Ioan Tomescu

    (Faculty of Mathematics and Computer Science, University of Bucharest, P. O. Box 050663, Bucharest, Romania)

  • Muhammad Imran

    (Department of Mathematical Sciences, United Arab Emirates University, P. O. Box 15551, Al Ain, UAE
    Department of Mathematics, School of Natural Sciences, NUST Islamabad, P. O. Box 24090, Islamabad, Pakistan)

  • Aisha Javed

    (Abdus Salam School of Mathematical Sciences, GC University, P. O. Box 54600, Lahore, Pakistan)

Abstract

For a graph G without isolated vertices, the inverse degree of a graph G is defined as I D ( G ) = ∑ u ∈ V ( G ) d ( u ) − 1 where d ( u ) is the number of vertices adjacent to the vertex u in G . By replacing − 1 by any non-zero real number we obtain zeroth-order general Randić index, i.e., 0 R γ ( G ) = ∑ u ∈ V ( G ) d ( u ) γ , where γ ∈ R − { 0 } . Xu et al. investigated some lower and upper bounds on I D for a connected graph G in terms of connectivity, chromatic number, number of cut edges, and clique number. In this paper, we extend their results and investigate if the same results hold for γ < 0 . The corresponding extremal graphs have also been identified.

Suggested Citation

  • Muhammad Kamran Jamil & Ioan Tomescu & Muhammad Imran & Aisha Javed, 2020. "Some Bounds on Zeroth-Order General Randić Index," Mathematics, MDPI, vol. 8(1), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:98-:d:306109
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    References listed on IDEAS

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    1. Guifu Su & Liming Xiong & Xiaofeng Su & Guojun Li, 2016. "Maximally edge-connected graphs and Zeroth-order general Randić index for $$\alpha \le -1$$ α ≤ - 1," Journal of Combinatorial Optimization, Springer, vol. 31(1), pages 182-195, January.
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