Title: Primitivity for graphs and matrices
Speaker: Dr. Rachel Quinlan, NUI Galway
A directed graph G is primitive if there is a positive integer k with the property that whenever u and v are vertices of the graph, there is a walk of length k from u to v in G. Equivalently, a non-negative square matrix A is primitive if there is a positive integer k for which all entries of A^k are positive. In both cases, the minimum such k is referred to as the exponent (of the graph or matrix). This talk will review some properties of primitive graphs and classical results about the range of possible exponents of a graph of order n, and also consider the class of minimally primitive graphs, which are primitive graphs that become imprimitive upon the deletion of any arc.
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