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Some results on Parikh word representable graphs and partitions
, Mathew Lisa, Bera Somnath, Subramanian K.G.
Published in Elsevier BV
Volume: 107
Pages: 102 - 115

Consequent to the introduction of the concept of Parikh matrix of a word which is based on the notion of subwords of a word, there has been an extensive research and study based on subwords. Parikh word representable graph is one such notion which has been introduced in the recent times. On the other hand connections of partitions of a number with counts of certain subword in a binary word are known. In this paper we introduce the notion of dual of a word and investigate its relationship with conjugate partition. As a result of this study, an expression for the number of nonisomorphic Parikh word representable graphs with a given number of edges, is obtained. Several other properties of Parikh word representable graphs are also derived.

About the journal
JournalData powered by TypesetAdvances in Applied Mathematics
PublisherData powered by TypesetElsevier BV
Open AccessNo