Walks in Graphs

Abstract

Given a finite set S and integer k≥0, let \(\binom{S}{k}\) denote the set of k-element subsets of S. A multiset may be regarded, somewhat informally, as a set with repeated elements, such as {1,1,3,4,4,4,6,}. We are only concerned with how many times each element occurs and not on any ordering of the elements. Thus for instance {2,1,2,4,1,2} and {1,1,2,2,2,4} are the same multiset: they each contain two 1’s, three 2’s, and one 4 (and no other elements).