Analyzing lattice networks through substructures

Lei, Hui; Li, Tao; Ma, Yuede; Wang, Hua

doi:10.1016/j.amc.2018.02.012

Cited by 16 publications

(7 citation statements)

References 33 publications

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“…Understanding key structural properties of large-scale data networks started to be crucial for analyzing and optimizing their performance, as well as improving their security. This topic has been attracting attention of many researches, recently (see [1,6,7,11]). We consider one of problems connected with the decomposition of networks into smaller pieces fulfilling some structural properties.…”

Section: Motivation and Preliminariesmentioning

confidence: 99%

Equitable d-degenerate Choosability of Graphs

Drgas-Burchardt

Furmańczyk

Sidorowicz

2020

Lecture Notes in Computer Science

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Let D d be the class of d-degenerate graphs and let L be a list assignment for a graph G. A colouring of G such that every vertex receives a colour from its list and the subgraph induced by vertices coloured with one color is a d-degenerate graph is called the (L,colouring is a generalization of an equitable list coloring, introduced by Kostochka et al., and an equitable list arboricity presented by Zhang. Such a model can be useful in the network decomposition where some structural properties on subnets are imposed. In this paper we give a polynomial-time algorithm that for a given (k, d)-partition of G with a t-uniform list assignment L and t ≥ k, returns its equitable (L, D d−1 )colouring. In addition, we show that 3-dimensional grids are equitably (L, D1)-colorable for any t-uniform list assignment L where t ≥ 3.

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Section: Motivation and Preliminariesmentioning

confidence: 99%

Equitable d-degenerate Choosability of Graphs

Drgas-Burchardt

Furmańczyk

Sidorowicz

2020

Lecture Notes in Computer Science

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“…The examples that involve the chemical applications of the topological index W p can be found in the papers [4,7–15]. Because of the considerable chemical applicability of the Wiener polarity index W p , this index has been the topic of various publications—see, for example, the recent papers [16–24], an excellent survey [25], and related references given therein.…”

Section: Introductionmentioning

confidence: 99%

On the second maximum Wiener polarity index of chemical trees of a fixed order

Ali

Zaineb

et al. 2021

Int J of Quantum Chemistry

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The Wiener polarity index Wp of a graph is defined as the number of unordered pairs of its vertices at distance 3. The problem of finding trees attaining the maximum Wp value, among all chemical trees of a fixed order n, was solved in the paper (Mol. Inf. 2019, 38, 1800076) for n ≥ 8. Motivated by the usage of Wp in a recent publication (J. Chem. Inf. Model. 2020, 60, 1224–1234), in this article we extend the work done in the aforementioned paper by giving a further ordering of chemical trees with respect to the maximum value of Wp. More precisely, we characterize the trees having the second maximum Wp value (which is 3n − 16) from the class of all chemical trees of a fixed order n, for n ≥ 9.

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“…Detail about the chemical applications of W p can be found in the papers [7,16,19,23,27,[29][30][31][32]. Considering the importance of this topological index, many researchers have devoted their attention towards it and studied its mathematical properties, for example see the papers [4,6,15,21,22,24,25,33,34] and references listed therein.…”

Section: Introductionmentioning

confidence: 99%

Towards the Solution of an Extremal Problem Concerning the Wiener Polarity Index of Alkanes

Noureen,

Bhatti,

Ali

2020

Preprint

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The Wiener polarity index W p , one of the most studied molecular structure descriptors, was devised by the chemist Harold Wiener for predicting the boiling points of alkanes. The index W p for chemical trees (chemical graphs representing alkanes) is defined as the number of unordered pairs of vertices at distance 3. A vertex of a chemical tree with degree at least 3 is called a branching vertex. A segment of a chemical tree T is a path-subtree S whose terminal vertices have degrees different from 2 in T and every internal vertex (if exists) of S has degree 2 in T . In this paper, the best possible sharp upper and lower bounds on the Wiener polarity index W p are derived for the chemical trees of order n with a given number of branching vertices or segments, and the corresponding extremal chemical trees are characterized. As a consequence of the derived results, an open problem concerning the maximal W p value of chemical trees with a fixed number of segments or branching vertices is solved.

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Analyzing lattice networks through substructures

Cited by 16 publications

References 33 publications

Equitable d-degenerate Choosability of Graphs

Equitable d-degenerate Choosability of Graphs

On the second maximum Wiener polarity index of chemical trees of a fixed order

Towards the Solution of an Extremal Problem Concerning the Wiener Polarity Index of Alkanes

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