New Sharp lower bounds for the first Zagreb index

Mansour, Toufik; Rostami, M. Ali; Suresh, E.; Xavier, G. Britto Antony

doi:10.5937/spsunp1601011m

Cited by 11 publications

(7 citation statements)

References 11 publications

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“…Remark 3.18 In [16], the present authors proved that Ψ * 1 and Ψ * 2 are incomparable. In addition, the lower bounds (3.19), (3.13), (3.20), and (3.14) are also incomparable respectively (Table 3): Next, we improve inequality (2.5) for the forgotten index F (G) using the harmonic index H(G).…”

Section: Theorem 316mentioning

confidence: 59%

On the bounds of the forgotten topological index

Elumalai¹,

Mansour²,

Rostami³

2017

Turk J Math

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The forgotten topological index is defined as the sum of cubes of the degrees of the vertices of the molecular graph G. In this paper, we obtain, analyze, and compare various lower bounds for the forgotten topological index involving the number of vertices, edges, and maximum and minimum vertex degree. Then we give Nordhaus-Gaddumtype inequalities for the forgotten topological index and coindex. Finally, we correct the number of extremal chemical trees on 15 vertices.

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Section: Theorem 316mentioning

confidence: 59%

On the bounds of the forgotten topological index

Elumalai¹,

Mansour²,

Rostami³

2017

Turk J Math

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“…wherefrom (21) is obtained. Equality in (22), and hence in (21), is attained if and only if α = β or d…”

Section: Resultsmentioning

confidence: 99%

“…The inequality (23) was proven in [19], the inequality (24) in [20], (25) in [7], (26) in [22], (27) in [6], (28) in [11]. The inequality (23) was proven in [13] for the case α = 2.…”

Section: Resultsmentioning

confidence: 99%

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Some inequalities for general zeroth-order Randic index

Milošević

Milovanovic

et al. 2019

Filomat

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v n }, be a simple connected graph with n vertices, m edges and vertex degree sequence ∆ = d 1 ≥ d 2 ≥ • • • ≥ d n = δ > 0, d i = d(v i). General zeroth-order Randić index of G is defined as 0 R α (G) = n i=1 d α i , where α is an arbitrary real number. In this paper we establish relationships between 0 R α (G) and 0 R α−1 (G) and obtain new bounds for 0 R α (G). Also, we determine relationship between 0 R α (G), 0 R β (G) and 0 R 2α−β (G), where α and β are arbitrary real numbers. By the appropriate choice of parameters α and β, a number of old/new inequalities for different vertex-degree-based topological indices are obtained.

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“…For the recent outcomes on Zagreb indices, see [8,17,3] and references therein. Li and Zheng [14] introduced the generalized version of the first Zagreb index.…”

Section: Introductionmentioning

confidence: 99%