Critical Groups and Line Graphs
نویسنده
چکیده
This paper is an overview of what the author has learned about the critical group of a graph, including some new results. In particular we discuss the critical group of a graph in relation to that of its line graph when the original graph is regular. We begin by introducing the critical group from various aspects. We then study the subdivision graph and line graph in relation to the critical group, the latter when the graph is regular. We discribe a homomorphism between the critcal groups of the line graph and the subdivision graph in this situation. Lastly, we conjecture some results about the kernel of this homomorphism and the structure of the critcal group of some particular graphs.
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