4 problems

Let $P_n$ be the path on $n$ vertices, and let $\{n,1\}$ be the non-edge joining its two ends. For simple graphs of order $n$, consider the derivative of Kemeny's constant…

Let $L_{r,s}$ denote a lollipop graph: a complete graph $K_r$ connected to a path graph on $s$ vertices by a bridge. For each $n$, consider simple graphs of order $n$ and the deriv…

Let $S$ be a denumerably infinite state space, and let $\{X_n\}_{n=0}^\infty$ be a positive recurrent, discrete-time Markov chain on $S$ with invariant probability measure $\mu$. F…

Infinitude conjecture. $K'$ is infinite for all infinite-state, discrete-time Markov chains.