The Mean Integrity of Paths and Cycles

作者：Ernst Claus^*; Rountree Beth

来源：Ars Combinatoria, 2010, 95: 499-509.

Let G be a graph with n vertices. The mean integrity of G is defined as follows: J(G) = min(P subset of VG) {vertical bar P vertical bar + (m) over tilde (G P)}, where (m) over tilde (G - P) = 1/n-vertical bar P vertical bar Sigma(nu is an element of VG-P) n(nu) and n(nu) is the size of the component containing nu. The main result of this article is a formula for the mean integrity of a path P(n) of n vertices. A corollary of this formula establishes the mean integrity of a cycle C(n) of n vertices.

• 出版日期2010-4