TY - JOUR

T1 - Some bounds on zeroth-order general randic index

AU - Jamil, Muhammad Kamran

AU - Tomescu, Ioan

AU - Imran, Muhammad

AU - Javed, Aisha

N1 - Funding Information:
Funding: This research is supported by the UPAR Grants of United Arab Emirates, Al-Ain, UAE via Grant No. G00002590 and Grant No. G00003271.
Publisher Copyright:
© 2020 by the authors.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - For a graph G without isolated vertices, the inverse degree of a graph G is defined as ID(G) = ∑u2V(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 Randic index, i.e., 0Rγ(G) = ∑u2V(G) d(u)γ, where γ ∈ R-System. Text. UTF8Encoding. Xu et al. investigated some lower and upper bounds on ID for a connected graph γ 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.

AB - For a graph G without isolated vertices, the inverse degree of a graph G is defined as ID(G) = ∑u2V(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 Randic index, i.e., 0Rγ(G) = ∑u2V(G) d(u)γ, where γ ∈ R-System. Text. UTF8Encoding. Xu et al. investigated some lower and upper bounds on ID for a connected graph γ 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.

KW - Extremal graphs

KW - Graph parameters

KW - Inverse degree

KW - Zeroth order general Randic index

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U2 - 10.3390/math8010098

DO - 10.3390/math8010098

M3 - Article

AN - SCOPUS:85080029115

VL - 8

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 1

M1 - 98

ER -