Number of walks and degree powers in a graph
  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. 
M. A. Fiol, E. Garriga
math.CO math.SP