New	bounds on the hyper-Zagreb index for the simple connected graphs

Elumalai, Suresh; Mansour, Toufik; Rostami, M. Ali

doi:10.5614/ejgta.2018.6.1.12

EJGTA

2018

DOI: 10.5614/ejgta.2018.6.1.12

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New bounds on the hyper-Zagreb index for the simple connected graphs

Suresh Elumalai¹,

Toufik Mansour

M. Ali Rostami

Abstract: The hyper-Zagreb index of a simple connected graph G is defined by

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Cited by 3 publications

References 15 publications

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Degree-based indices of hypergraphs: Definitions and first results

Vetrík

2024

Asian-European J. Math.

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For a [Formula: see text]-uniform hypergraph [Formula: see text], we introduce degree-based indices such as the general sum-connectivity index [Formula: see text] and the general Randić index [Formula: see text], where [Formula: see text], [Formula: see text] is the set of hyperedges of [Formula: see text] and [Formula: see text] is the degree of a vertex [Formula: see text] in [Formula: see text]; [Formula: see text] and [Formula: see text]. Other indices such as the first and second Zagreb index, first and second hyper-Zagreb index, classical sum-connectivity index, classical Randić index and harmonic index of a hypergraph [Formula: see text] are special cases of the general indices. For [Formula: see text], we obtain upper bounds on [Formula: see text] and [Formula: see text] for a uniform hypergraph [Formula: see text] with given order, order and number of isolated vertices, order and maximum degree, order and diameter at least [Formula: see text], and lower bounds for uniform hypergraphs with given order and no isolated vertices, order and minimum degree, and order and maximum possible degree. We also present extremal graphs for all the bounds. Bounds on Zagreb indices follow from our results on general indices.

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Degree-based indices of hypergraphs: Definitions and first results

Vetrík

2024

Asian-European J. Math.

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Generalized Quasi Trees with Respect to Degree Based Topological Indices and Their Applications to COVID-19 Drugs

Altassan

Imran

2023

Mathematics

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The l-generalized quasi tree is a graph G for which we can find W⊂V(G) with |W|=l such that G−W is a tree but for an arbitrary Y⊂V(G) with |Y|<l, G−Y is not a tree. In this paper, inequalities with respect to zeroth-order Randić and hyper-Zagreb indices are studied in the class of l-generalized quasi trees. The corresponding extremal graphs corresponding to these indices in the class of l-generalized quasi trees are also obtained. In addition, we carry QSPR analysis of COVID-19 drugs with zeroth-order Randić and hyper-Zagreb indices (energy).

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HZ-Coindex for the Sum-Graphs under Cartesian Product

2022

Punjab Univ. j. math.

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:Let G = (V (G), E(G)) be a simple connected graph with V (G) and E(G) as the vertex and edge sets respectively. The physical and structural properties of the graphs are discussed with different mathematical tools, One of them is topological index (TI) and it can be obtained directly from molecular structures and rapidly computed for large number of molecules. Graph operations play an important role in the development of various new classes of graphs. If G is a connected simple graph then we obtained new graphs by applying various operations on G such as S subdivided, R triangle parallel, Q line superposition and T total graphs operations on G. In this paper, we computed the hyper Zagreb coindex of derived graphs in the form of their factor graphs. At the end, we have analyzed our results by the numerical tables for the particular generalized D-sum graphs

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New bounds on the hyper-Zagreb index for the simple connected graphs

Abstract: The hyper-Zagreb index of a simple connected graph G is defined by

Cited by 3 publications

References 15 publications

Degree-based indices of hypergraphs: Definitions and first results

Degree-based indices of hypergraphs: Definitions and first results

Generalized Quasi Trees with Respect to Degree Based Topological Indices and Their Applications to COVID-19 Drugs

HZ-Coindex for the Sum-Graphs under Cartesian Product

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