On Core Words and the Parikh Matrix Mapping

Teh, Wen Chean

doi:10.1142/s0129054115500069

Cited by 23 publications

(8 citation statements)

References 17 publications

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“…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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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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“…On the other hand, in the study of numerical quantities related to subwords (also called scattered subwords) of a word, the notion of Parikh matrix of a word over an ordered alphabet was introduced in [25]. This has opened up a new direction of research in the area of combinatorics on words [22] and many problems on words and subwords have been investigated (see, for example, [1,2,24,32,33,34,36,37,38] and references therein), resulting in a number of interesting results. Parikh word representable graph (P W RG) is one such notion introduced in [3] linking the two areas of study on properties of words and of graphs.…”

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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“…However, not every word is uniquely determined by its Parikh matrix. The injectivity problem, which asks for a characterization of words sharing the same Parikh matrix, has received extensive interest (for example, see [1][2][3][4][5][6][7][14][15][16][17][18][19][20][21][22]). This, together with the fact that Parikh matrices are dependent on the ordering of the alphabet, led to the introduction of strong M-equivalence in [18].…”

Section: Introductionmentioning

confidence: 99%

Strong (2 ⋅ t) and Strong (3 ⋅ t) Transformations for Strong M-Equivalence

Poovanandran

Teh

2019

Int. J. Found. Comput. Sci.

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Parikh matrices have been extensively investigated due to their usefulness in studying subword occurrences in words. Due to the dependency of Parikh matrices on the ordering of the alphabet, strong M-equivalence was proposed as an order-independent alternative to M-equivalence in studying words possessing the same Parikh matrix. This paper introduces and studies the notions of strong (2 · t) and strong (3 · t) transformations in determining when two ternary words are strongly M-equivalent. The irreducibility of strong (2·t) transformations are then scrutinized, exemplified by a structural characterization of irreducible strong (2 · 2) transformations. The common limitation of these transformations in characterizing strong M-equivalence is then addressed.2010 Mathematics Subject Classification. 68R15, 68Q45, 05A05. Key words and phrases. Parikh matrices, subword, injectivity problem, strong M-equivalence.* The choice of term is due to the fact that this transformation is an analogue of the (2 · t) transformation, introduced by Atanasiu in [2].

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On Core Words and the Parikh Matrix Mapping

Cited by 23 publications

References 17 publications

Certain Distance-Based Topological Indices of Parikh Word Representable Graphs

Certain Distance-Based Topological Indices of Parikh Word Representable Graphs

Wiener-type indices of Parikh word representable graphs

Strong (2 ⋅ t) and Strong (3 ⋅ t) Transformations for Strong M-Equivalence

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