Graph Labelings Obtainable by Random Walks

文献摘要

\sum_{k = 0}^{n - 1} 2^{k} (2 k + 1)^{- 1} {(\binom{2 k}{k})}^{- 1} (\binom{n + k}{k}) = (\binom{2 n}{n}) 2^{- n} \sum_{k = 0}^{n - 1} 2^{k} (2 k + 1)^{- 1} {(\binom{2 k}{k})}^{- 1}

We initiate the study of what we refer to as random walk labelings of graphs. These are graph labelings that are obtainable by performing a random walk on the graph, such that the labeling occurs increasingly whenever an unlabeled vertex is encountered. Some of the results we obtain involve sums of inverses of binomial coefficients, for which we obtain new identities. In particular, we prove that $\sum_{k = 0}^{n - 1} 2^{k} (2 k + 1)^{- 1} {(\binom{2 k}{k})}^{- 1} (\binom{n + k}{k}) = (\binom{2 n}{n}) 2^{- n} \sum_{k = 0}^{n - 1} 2^{k} (2 k + 1)^{- 1} {(\binom{2 k}{k})}^{- 1}$ , thus confirming a conjecture of Bala.

Graph Labelings Obtainable by Random Walks

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Graph Labelings Obtainable by Random Walks

文献摘要

讨论

讲解博客

AI智能校验

Graph Labelings Obtainable by Random Walks

文献摘要

讨论

|讲解博客

|AI智能校验

Graph Labelings Obtainable by Random Walks

文献摘要

讨论

|讲解博客

|AI智能校验

讲解博客

AI智能校验

讲解博客

AI智能校验