Title: Kemeny’s constant for random walks on graphs
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Abstract: Kemeny's constant, a fundamental parameter in the theory of Markov chains, has recently received significant attention within the graph theory community. Originally defined for a discrete, finite, time-homogeneous, and irreducible Markov chain based on its stationary vector and mean first passage times, Kemeny's constant finds special relevance in the study of random walks on graphs. Kemeny's constant gives a measure of how quickly a random walker can move around a graph, and is thus a good measure of the connectivity of a graph. It is natural to study how graph structure informs a graph invariant. In this talk, we will understand how graph structures provide insights into Kemeny’s constant. In addition, we will also examine how the addition of an edge affects Kemeny’s constant.