Some Bounds on Zeroth-Order General Randi? Index

Muhammad Kamran Jamil, Ioan Tomescu, Muhammad Imran and Aisha Javed
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Muhammad Kamran Jamil: Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, P. O. Box 54600, Lahore, Pakistan
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
Aisha Javed: Abdus Salam School of Mathematical Sciences, GC University, P. O. Box 54600, Lahore, Pakistan

Mathematics, 2020, vol. 8, issue 1, 1-12

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 Randi? 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.

Keywords: inverse degree; zeroth order general Randi? index; extremal graphs; graph parameters (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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