On the Representability of Line Graphs
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) ∈ E for each x ≠ y. Such a W is called a word-representant of G. Note that in this paper we use the term graph to mean a finite, simple graph, even though the definition of representable is applicable to more general graphs.
KeywordsLine Graph Simple Graph General Graph Circle Graph External Vertex
- 2.Halldórsson, M., Kitaev, S., Pyatkin, A.: On representable graphs, semi-transitive orientations, and the representation numbers, arXiv:0810.0310v1 (math.CO) (2008)Google Scholar
- 4.Kitaev, S., Pyatkin, A.: On representable graphs. Automata, Languages and Combinatorics 13, 1, 45–54 (2008)Google Scholar
- 5.Kitaev, S., Seif, S.: Word problem of the Perkins semigroup via directed acyclic graphs. Order (2008), doi:10.1007/s11083-008-9083-7Google Scholar