6 papers
Line Graphs of Non-Word-Representable Graphs are Not Always Non-Word-Representable
Khyodeno Mozhui, Tithi Dwary, K. V. Krishna
A graph is said to be word-representable if there exists a word over its vertex set such that any two vertices are adjacent if and only if they alternate in the word. If no such wo…
Characterization of Split Comparability Graphs
Tithi Dwary, Khyodeno Mozhui, K. V. Krishna
A split graph is a graph whose vertex set can be partitioned into a clique and an independent set. A split comparability graph is a split graph which is transitively orientable. In…
Representation Number of Word-Representable Split Graphs
Tithi Dwary, Khyodeno Mozhui, K. V. Krishna
A split graph is a graph whose vertex set can be partitioned into a clique and an independent set. The word-representability of split graphs was studied in a series of papers in th…
Word-Representability of Well-Partitioned Chordal Graphs
Tithi Dwary, K. V. Krishna
In this paper, we study the word-representability of well-partitioned chordal graphs using split decomposition. We show that every component of the minimal split decomposition of a…
Characterization of Word-Representable Graphs using Modular Decomposition
Tithi Dwary, K. V. Krishna
In this work, we characterize the class of word-representable graphs with respect to the modular decomposition. Consequently, we determine the representation number of a word-repre…
Characterization of Double-Arborescences and their Minimum-Word-Representants
Tithi Dwary, K. V. Krishna
A double-arborescence is a treelike comparability graph with an all-adjacent vertex. In this paper, we first give a forbidden induced subgraph characterization of double-arborescen…