The Critical Group of a Line Graph
نویسندگان
چکیده
منابع مشابه
The Critical Group of a Line Graph
The critical group of a graph is a finite abelian group whose order is the number of spanning forests of the graph. This paper provides three basic structural results on the critical group of a line graph. • The first deals with connected graphs containing no cut-edge. Here the number of independent cycles in the graph, which is known to bound the number of generators for the critical group of ...
متن کاملA Note on the Critical Group of a Line Graph
This note answers a question posed by Levine in [3]. The main result is Theorem 1 which shows that under certain circumstances a critical group of a directed graph is the quotient of a critical group of its directed line graph.
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The critical group of a connected graph is a finite abelian group, whose order is the number of spanning trees in the graph. The structure of this group is a subtle isomorphism invariant that has received much attention recently, partly due to its relation to the graph Laplacian and chip-firing games. However, the group structure has been determined for relatively few classes of graphs. We conj...
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ژورنال
عنوان ژورنال: Annals of Combinatorics
سال: 2012
ISSN: 0218-0006,0219-3094
DOI: 10.1007/s00026-012-0141-x