New bounds for the sum of powers of normalized Laplacian eigenvalues of graphs

Clemente, Gian Paolo; Cornaro, Alessandra

doi:10.26493/1855-3974.845.1b6

Cited by 10 publications

(8 citation statements)

References 15 publications

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“…It was empirically determined Since the k-th spectral moment of a graph is equal to the number of self-returning walks of the length k, 31 the relations between spectral moments for k = 0, 2, and 4 and some other, easily divisible graph invariants, are derived years ago (e.g. see 32 ): (10) where n, and Zg 1 (T) are the number of vertices and the first Zagreb index of a tree T.…”

Section: Estrada Index Versus Resolvent Energymentioning

confidence: 99%

“…Incorporating equations shown in (10) into (9), the formula, relating the resolvent energy of a graph, Estrada index and the first Zagreb index, is obtained: (11) In order to get the fitting parameter α that appears in (11), we made an in-house computer program. This program is written in Python and the α values are obtained for all chemical trees from 6 to 20 vertices.…”

Section: Estrada Index Versus Resolvent Energymentioning

confidence: 99%

“…This invoked the introduction of many other Estrada-like invariants. 10,[17][18][19] Recently, another topological invariant based on "ordinary" eigenvalues has been introduced. 20 This descriptor is named resolvent energy after the resolvent matrix which eigenvalues are used in its definition.…”

Section: Introductionmentioning

confidence: 99%

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On Relationships of Eigenvalue–Based Topological Molecular Descriptors

Redžepović¹,

Furtula

2020

ACSi

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Three eigenvalue-based topological molecular descriptors are compared using several datasets of alkanes. Two of them are well-known and frequently employed in various QSPR/QSAR investigations, and third-one is a newly derived whose predictive potential is yet to be proven. The relations among them are found and discussed. Structural parameters that govern these relations are identified and the corresponding formulas based on multiple linear regression have been obtained. It has been shown that all three investigated indices are encoding almost the same structural information of a molecule. They differ only by the extent of the sensitivity on a structural branching of a molecule and on the number of non-bonding molecular orbitals.

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Section: Estrada Index Versus Resolvent Energymentioning

confidence: 99%

Section: Estrada Index Versus Resolvent Energymentioning

confidence: 99%

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On Relationships of Eigenvalue–Based Topological Molecular Descriptors

Redžepović¹,

Furtula

2020

ACSi

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“…Some techniques to determine the Kirchhoff index and multiplicative degree-Kirchhoff index were given in [2,3,7,8,25]. Some other topics on the Kirchhoff index and the multiplicative degree-Kirchhoff index of a graph may be referred to [26,30,34,36,37] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Resistance distance-based graph invariants and spanning trees of graphs derived from the strong product of $P_2$ and $C_n$

Pan,

2019

Preprint

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Let G n be a graph obtained by the strong product of P 2 and C n , where n 3. In this paper, explicit expressions for the Kirchhoff index, multiplicative degree-Kirchhoff index and number of spanning trees of G n are determined, respectively. It is surprising to find that the Kirchhoff (resp. multiplicative degree-Kirchhoff) index of G n is almost one-sixth of its Wiener (resp. Gutman) index. Moreover, let G r n be the set of subgraphs obtained from G n by deleting any r vertical edges of G n , where 0 r n. Explicit formulas for the Kirchhoff index and the number of spanning trees for any graph G r n ∈ G r n are completely established, respectively. Finally, it is interesting to see that the Kirchhoff index of G r n is almost one-sixth of its Wiener index.

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“…In particular, we employ a theoretical methodology proposed by Bianchi and Torriero in [19] based on nonlinear global optimization problems solved through majorization techniques. These bounds can also be quantified by using the numerical approaches developed in [20] and [21] and extended for the normalized Laplacian matrix in [22] and in [23]. …”

Section: Introductionmentioning

confidence: 99%

Bounding the HL-index of a graph: a majorization approach

Clemente

Cornaro

2016

J Inequal Appl

Self Cite

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In mathematical chemistry, the median eigenvalues of the adjacency matrix of a molecular graph are strictly related to orbital energies and molecular orbitals. In this regard, the difference between the occupied orbital of highest energy (HOMO) and the unoccupied orbital of lowest energy (LUMO) has been investigated (see Fowler and Pisansky in Acta Chim. Slov. 57:513-517, 2010). Motivated by the HOMO-LUMO separation problem, Jaklič et al. in (Ars Math. Contemp. 5:99-115, 2012) proposed the notion of HL-index that measures how large in absolute value are the median eigenvalues of the adjacency matrix. Several bounds for this index have been provided in the literature. The aim of the paper is to derive alternative inequalities to bound the HL-index. By applying majorization techniques and making use of some known relations, we derive new and sharper upper bounds for this index. Analytical and numerical results show the performance of these bounds on different classes of graphs.

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New bounds for the sum of powers of normalized Laplacian eigenvalues of graphs

Cited by 10 publications

References 15 publications

On Relationships of Eigenvalue–Based Topological Molecular Descriptors

On Relationships of Eigenvalue–Based Topological Molecular Descriptors

Resistance distance-based graph invariants and spanning trees of graphs derived from the strong product of $P_2$ and $C_n$

Bounding the HL-index of a graph: a majorization approach

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