Number of walks and degree powers in a graph |
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| Authors: | MA Fiol E Garriga |
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| Institution: | Departement de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, Jordi Girona 1-3, Mòdul C3, Campus Nord, 08034 Barcelona, Catalonia, Spain |
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| Abstract: | This note deals with the relationship between the total number of k-walks in a graph, and the sum of the k-th powers of its vertex degrees. In particular, it is shown that the the number of all k-walks is upper bounded by the sum of the k-th powers of the degrees. |
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| Keywords: | Graph Walks Degree powers Adjacency matrix Laplacian matrix |
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