Histories in path graphs
Ludovít Niepel
Discussiones Mathematicae Graph Theory, Tome 27 (2007), p. 345-357 / Harvested from The Polish Digital Mathematics Library
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For a given graph G and a positive integer r the r-path graph, Pr(G), has for vertices the set of all paths of length r in G. Two vertices are adjacent when the intersection of the corresponding paths forms a path of length r-1, and their union forms either a cycle or a path of length k+1 in G. Let Prk(G) be the k-iteration of r-path graph operator on a connected graph G. Let H be a subgraph of Prk(G). The k-history Pr-k(H) is a subgraph of G that is induced by all edges that take part in the recursive definition of H. We present some general properties of k-histories and give a complete characterization of graphs that are k-histories of vertices of 2-path graph operator.

Publié le : 2007-01-01
EUDML-ID : urn:eudml:doc:270721 
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Ludovít Niepel. Histories in path graphs. Discussiones Mathematicae Graph Theory, Tome 27 (2007) pp. 345-357. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1366/

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