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Word-Representability of Line Graphs

2011
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Open Journal of Discrete Mathematics
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A graph G=(V,E) is representable if there exists a word W over the alphabet V such that letters x and y alternate in W if and only if (x,y) is in E for each x not equal to y. The motivation to study representable graphs came from algebra, but this subject is interesting from graph theoretical, computer science, and combinatorics on words points of view. In this paper, we prove that for n greater than 3, the line graph of an n-wheel is non-representable. This not only provides a new construction

doi:10.4236/ojdm.2011.12012
fatcat:mcmawfz77rdnfjyepbiiipe5ga