Structural Properties of Word Representable Graphs

Bera, Somnath; Mahalingam, Kalpana

doi:10.1007/s11786-016-0257-1

Cited by 12 publications

(22 citation statements)

References 11 publications

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“…We have derived formulas for evaluating the Wiener index and certain other variants of Wiener topological indices for Parikh word representable graphs [3] of binary core words. There are problems that remain to be investigated.…”

Section: Resultsmentioning

confidence: 99%

“…We now recall the notion of Parikh word representable graph (P W RG) [3]. For basic concepts pertaining to graphs we refer to [4].…”

Section: Preliminariesmentioning

confidence: 99%

“…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. 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].…”

Section: Introductionmentioning

confidence: 99%

“…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. 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%

“…[3] For a word w = a 1 a 2 • • • a n of length n where for 1 ≤ i ≤ n, a i ∈ Σ = {a < b}, we associate a simple graph G = G(w) with n vertices {1, 2, • • • , n}.…”

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confidence: 99%

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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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Section: Resultsmentioning

confidence: 99%

“…We now recall the notion of Parikh word representable graph (P W RG) [3]. For basic concepts pertaining to graphs we refer to [4].…”

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…[3] For a word w = a 1 a 2 • • • a n of length n where for 1 ≤ i ≤ n, a i ∈ Σ = {a < b}, we associate a simple graph G = G(w) with n vertices {1, 2, • • • , n}.…”

mentioning

confidence: 99%

See 3 more Smart Citations

Wiener-type indices of Parikh word representable graphs

Thomas¹,

Mathew²,

Sriram

et al. 2021

Ars Math. Contemp.

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Critical properties of bipartite permutation graphs

Alecu

Malyshev

2023

Journal of Graph Theory

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The class of bipartite permutation graphs enjoys many nice and important properties. In particular, this class is critically important in the study of clique‐ and rank‐width of graphs, because it is one of the minimal hereditary classes of graphs of unbounded clique‐ and rank‐width. It also contains a number of important subclasses, which are critical with respect to other parameters, such as graph lettericity or shrub‐depth, and with respect to other notions, such as well‐quasi‐ordering or complexity of algorithmic problems. In the present paper we identify critical subclasses of bipartite permutation graphs of various types.

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