CMMSE 18: geometric-arithmetic index and line graph

Pestana, Domingo; Sigarreta, José M.; Tourís, Eva

doi:10.1007/s10910-018-00993-z

Cited by 12 publications

(6 citation statements)

References 21 publications

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“…They are an active topic of research at this moment. In particular, several papers study some topological indices on line graphs (see, e.g., [44,45]).…”

Section: Id Polynomials Of Other Graph Operationsmentioning

confidence: 99%

f-Polynomial on Some Graph Operations

et al. 2019

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Given any function f : Z + → R + , let us define the f-index I f ( G ) = ∑ u ∈ V ( G ) f ( d u ) and the f-polynomial P f ( G , x ) = ∑ u ∈ V ( G ) x 1 / f ( d u ) − 1 , for x > 0 . In addition, we define P f ( G , 0 ) = lim x → 0 + P f ( G , x ) . We use the f-polynomial of a large family of topological indices in order to study mathematical relations of the inverse degree, the generalized first Zagreb, and the sum lordeg indices, among others. In this paper, using this f-polynomial, we obtain several properties of these indices of some classical graph operations that include corona product and join, line, and Mycielskian, among others.

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“…They are an active topic of research at this moment. In particular, several papers study some topological indices on line graphs (see, e.g., [44,45]).…”

Section: Id Polynomials Of Other Graph Operationsmentioning

confidence: 99%

f-Polynomial on Some Graph Operations

et al. 2019

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“…Although it was introduced in 2009, there are many papers dealing with this index (see, e.g., [9], [10], [18], [22], [25], [28], [32], [33], [34], [40] and the references therein). The predicting ability of the GA index compared with Randić index is reasonably better (see [9,Table 1]).…”

Section: Mathematics Subject Classification (2010) 05c09 • 05c92 1 In...mentioning

confidence: 99%

Analytical and computational study of the variable inverse sum deg index

Carballosa¹,

Méndez-Bermúdez²,

Rodríguez³

et al. 2021

Preprint

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A large number of graph invariants of the form uv∈E(G) F (d u , d v ) are studied in mathematical chemistry, where uv denotes the edge of the graph G connecting the vertices u and v, and d u is the degree of the vertex u. Among them the variable inverse sum deg index ISD a , with), was found to have applicative properties. The aim of this paper is to obtain new inequalities for the variable inverse sum deg index, and to characterize graphs extremal with respect to them. Some of these inequalities generalize and improve previous results for the inverse sum indeg index. In addition, we computationally validate some of the obtained inequalities on ensembles of random graphs and show that the ratio ISD a (G) /n (n being the order of the graph) depends only on the average degree d .

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“…Line graphs were initially introduced by Whitney in [21] and a few year later by Krausz in his work [22], however the first time that the exact terminology of line graph was used, it was in the joint work by Harary and Norman in [23]. Nowadays this is an active topic, where we can find very recent works that study some topological indices on line graphs (see, e.g., [24,25]). If G is a regular graph is regular, then the both bounds are the same, and they are equal to GA 1 (G).…”

Section: Theoremmentioning

confidence: 99%