Some results on Parikh word representable graphs and partitions

Mathew, Lisa; Thomas, Nobin; Bera, Somnath; Subramanian, K. G.

doi:10.1016/j.aam.2019.02.009

Cited by 7 publications

(3 citation statements)

References 10 publications

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“…Furthermore, chemical graph theory has sparked interest in various topological indices associated with graphs, aiming to describe molecular structures in terms of these indices [23][24][25][26][27][28][29]. Numerous studies have provided formulas for computing these indices and established constraints on their values [30,31].…”

Section: Introductionmentioning

confidence: 99%

On Exploring the Topological Aspects of the Chemical Structure of the Nanotube \(HAC_{5}C_{7}[w,t]\)

Zakir,

Naseer,

Farahani

et al. 2024

Util. Math.

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Graph theory has experienced notable growth due to its foundational role in applied mathematics and computer science, influencing fields like combinatorial optimization, biochemistry, physics, electrical engineering (particularly in communication networks and coding theory), and operational research (with scheduling applications). This paper focuses on computing topological properties, especially in molecular structures, with a specific emphasis on the nanotube \(HAC_{5}C_{7}[w,t]\)

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Section: Introductionmentioning

confidence: 99%

On Exploring the Topological Aspects of the Chemical Structure of the Nanotube \(HAC_{5}C_{7}[w,t]\)

Zakir,

Naseer,

Farahani

et al. 2024

Util. Math.

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show abstract

“…Among various studies that involve graphs for analyzing and solving different kinds of problems, relating words that are finite sequences of symbols with graphs is an interesting area of investigation (for example, [1][2][3][4][5]). Based on the notion of subwords (also called scattered subwords) of a word and the concept of a matrix called Parikh matrix of a word, introduced in [6] and intensively investigated by many researchers (for example, [7][8][9][10][11][12][13] and references therein) with entries of the Parikh matrix giving the counts of certain subwords in a word, a graph called Parikh word representable graph (PWRG) of a word, was introduced in [14] and its relationship with the corresponding word and partition was studied in [15].…”

Section: Introductionmentioning

confidence: 99%

Certain Distance-Based Topological Indices of Parikh Word Representable Graphs

Thomas

Mathew²,

Sriram

et al. 2021

Journal of Mathematics

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Relating graph structures with words which are finite sequences of symbols, Parikh word representable graphs (PWRGs) were introduced. On the other hand, in chemical graph theory, graphs have been associated with molecular structures. Also, several topological indices have been defined in terms of graph parameters and studied for different classes of graphs. In this study, we derive expressions for computing certain topological indices of PWRGs of binary core words, thereby enriching the study of PWRGs.

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“…Based on the notions of subwords of a word and the Parikh matrix of a word [25] with entries of the matrix giving the counts of certain subwords in the word, P W RG related to a word was introduced in [3]. Relationship of these graphs with corresponding words and partitions was recently studied in [26].…”

Section: Introductionmentioning

confidence: 99%

Wiener-type indices of Parikh word representable graphs

Thomas¹,

Mathew²,

Sriram

et al. 2021

Ars Math. Contemp.

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A new class of graphs G(w), called Parikh word representable graphs (P W RG), corresponding to words w that are finite sequence of symbols, was considered in the recent past. Several properties of these graphs have been established. In this paper, we consider these graphs corresponding to binary core words of the form aub over a binary alphabet {a, b}. We derive formulas for computing the Wiener index of the P W RG of a binary core word. Sharp bounds are established on the value of this index in terms of different parameters related to binary words over {a, b} and the corresponding P W RGs. Certain other Wiener-type indices that are variants of Wiener index are also considered. Formulas for computing these indices in the case of P W RG of a binary core word are obtained.

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Some results on Parikh word representable graphs and partitions

Cited by 7 publications

References 10 publications

On Exploring the Topological Aspects of the Chemical Structure of the Nanotube \(HAC_{5}C_{7}[w,t]\)

On Exploring the Topological Aspects of the Chemical Structure of the Nanotube \(HAC_{5}C_{7}[w,t]\)

Certain Distance-Based Topological Indices of Parikh Word Representable Graphs

Wiener-type indices of Parikh word representable graphs

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